It is highly recommended that you get a good soil test before adding soil amendments and fertilizers if a 500-pound pumpkin is your highest goal you may be fine using a balanced fertilizer and nothing else. Each advancement in your growing techniques will bring you more pounds and bigger rewards. Soil samples are usually taken from several locations in your garden then they are mixed together and a small sample is shipped to a laboratory. Western Laboratories Inc (Link*1)has a soil test specifically for Giant Pumpkins and as of now costs $55. They will email you a report that tells you what and how much you should use.
              The method you use to fertilizer your plants can vary and may depend on your irrigation method. You may choose to water/fertilize just by watering can, a lawn sprinkler, a hose-end sprayer or a drip irrigation method. Giant pumpkins love water a 1000sqft plant may use 30 to 100 gallons a day during peak growth. If possible fill a tank with water and let it sit for 24 hours this allows chlorine from your city water to evaporate plus it allows the water to warm up. Fertilizers can be added to the tank as well while different devices can be attached to irrigation lines that will mix fertilizer for you, a venturi injector (see link*2 below)will run $12 to $30 and a Dosatron In-Line Fertilizer Injector $350 or more .
                Try to keep your giant pumpkin/watermelons and other fruits growing at a steady pace, if you fertilize heavily once every two weeks you may cause it to break from a surge of growth. Once per week is better but feeding a little each day is the best. One teaspoon per day may be enough for a plant covering 1000sqft. if your fertilizer calls for X amount every two weeks divide that amount by 14 if you’re using it daily. For pumpkins spread the fertilizer and water out under the entire plant and do the areas that the plant hasn’t reached yet, roots grow well outside the leafy area.
               Near perfect garden conditions for AG (Atlantic Giant) pumpkins would be in the range like below Don’t worry if yours are not, it’s all about the ratios between the nutrients, it is very difficult to impossible to lower the level of a nutrient in soil, so if one type is too high, you can bring up the others to be in the correct ratio. If you use Bryan Langley’s soil estimator (video *3) you can see what happens as you add nutrients to your soil, it is explained by Cecil Weston in (video*4)

Organic Matter (OM) 8-9%
Nitrogen (N) 30-35 ppm
Phosphorus (P) 160-170 ppm
Potassium (K) 540-550 ppm
Magnesium (Mg) 310-320 ppm
Calcium (Ca) 2540-2550 ppm pH 6.9-7.0
CEC (Cation Exchange Capacity) 16-17%
Potassium Base Saturation (K%) 8-9%
MagnesiumBase Saturation (Mg%) 20-21%
Calcium Base Saturation (Ca%) 66-67%
Sulfur (S) 49-50 ppm
Zinc (Z) 9-10 ppm
Manganese (Mn) 25-26 ppm
Iron (Fe) 46-47 ppm
Copper (Cu) 2-2.3 ppm
Boron (B) 1-2. ppm

The numbers..1–2–4
                          N–P-K
The first number is the percentage of Nitrogen(N) in the product (primary use is for plant growth)
The second number is the percentage of Phosphorus(P) in the product (primary use root and flower growth,)
The third number is the percentage of Potassium(K) in the product (primary use for fruit growth)

The way the numbers may be written can vary if its an 18-0-0 product it contains 18 percent Nitrogen or may be written as 18% or .18 Timing, your fertilizer is important, a plant grows in cycles rooting-plant growth-flowering and fruit set and fruit growth The fertilizer ratios below can vary greatly, an example is given as a general idea of what you may need.If you only want one product use a balanced fertilizer like 10-10-10

Plants in containers for less than 3 weeks do not need to be fertilized ( in most cases)
For rooting
Let your plant be in the ground for one week then use a phosphorus fertilizer (15-30-15) or some growers use Bud
and Bloom 5-50-17 whichever product you have, use it at ¼ the recommended amount Wait one week and fertilize
again at ½ the recommended amount, this will promote root growth, now switch to a higher Nitrogen(N) fertilizer

For plant growth
Nitrogen(N) is usually given in extra amounts after the plant has been in the ground for two or three weeks, something like 20-10-10 will promote the growth of the leaves and vines, lesser amounts are used two weeks before flowering. Too much N can prevent flower production and may lead to aborting fruit, but the plant still needs N during all growth stages. If leaves begin to pale or leaf growth stops increase the N again. Plants are able to use calcium nitrate(15-0-0) better than Ammonium Sulfate(21-0-0) when the soil is cold

For flowering
Phosphorus is needed for flower and fruit growth so it should be used at this time, just two types would be the 5-50-17 if you already have it or 15-30-15 Nitrogen is lowered to prevent aborting fruits and flower loss but monitor the plant for changes in color if leaves begin to pale use more N if they get too dark or the leaves look bloated cut back on the N. Phosphorus can build up to high in the soil, it doesn’t leach away easily unlike N that needs to be constantly added, too much (P) can throw out the balance of your soil and take years to correct

Fruit growth
Once your pumpkin begins growing rapidly you can use a fertilizer slightly higher in Potassium(K) An example would be 5-11-26 If at some point you think your plant needs a boost of N a foliar application of fish fertilizer may be all you need. You can apply it every 6 days until the color improves. Some growers do not recommend using fish fertilizer before the pumpkin is set and growing as it may supply too much nitrogen and stop flowering. Neptune’s Harvest fish formula is a popular fertilizer

If soil temperatures are too low your plant will not be able to absorb enough nutrients through its roots this can be a  problem when planting early season when the soil temperature is below 60F. The plant’s leaf color may lighten and most growth stops. You can apply Magnesium (Epsom salts) and nitrogen through foliar feeding. Use a nitrogen fertilizer at ½ strength and add 2 tsp of Epsom salts to the gallon of water. Then foliar spray the top and bottom of the leaves. This is just one reason why many growers use soil warming cables. Plants are able to use calcium nitrate(15-0-0) better than Ammonium Sulfate(21-0-0) when the soil is cold

Common products used for amending soil (others are available)
21-0-0 Ammonium Sulfate+24% sulfur Classification Synthetic (non-organic)Lowers PH
34-0-0 Ammonium Nitrate Classification Synthetic (non-organic)May raise PH but mostly neutral
15-0-0 Calcium Nitrate Classification Synthetic (non-organic)May raise PH but mostly neutral
11-52-0 MAP monoammonium phosphate + 18% sulfur Classification Synthetic (non-organic)Lowers PH
0-52-34 Monopotassium Phosphate Classification Synthetic (non-organic)may lower PH if its above7.2
0-0-50 Potassium sulfate +18% sulfur Most are not organic but some are,it depends on the manufacturing
process, it does not change PH
0-45-0 Triple Super Phosphate Classification Synthetic (non-organic)
Iron sulfate (ferrous sulfate) 20% Organic lowers PH
Zinc Sulfate Monohydrate — 35.5% Organic Allowed with Restrictions
Manganese Sulfate Powder – 32% Organic Allowed with Restrictions
99%pure copper sulfate is 25% copper Allowed in organic gardens with Restrictions
Magnesium (Epsom salts) 11% Allowed in organic gardens Synthetic/Nonsynthetic
Boron 11% mule team borax Allowed in organic gardens with Restrictions
Plant dusting sulfur Allowed in organic gardens with Restrictions (non- soil use)
Elemental Sulphur Allowed in organic gardens with Restrictions —lowers PH
You can look up products to see if they are organic at (link*5)

(*1) Western Laboratories INC         https://westernlaboratories.com/
(*2) Venturi injector                            https://www.amazon.com/s?k=Venturi+injector&ref=nb_sb_noss
Fertilizer siphon injector                   https://www.amazon.com/s?k=fertilizer+siphon+injector&ref=nb_sb_noss
Dosatron fertilizer injector                https://www.dosatronusa.com/
(*3) Soil Estimator                                http://www.team-pumpkin.org/downloads.htm
(*4) Soil Estimator explained             https://www.youtube.com/watch?v=g8opfz9e3h0
(*5) Organic Materials Review Institute   https://www.omri.org/