2-3 gallons doesn't seem like nearly enough strike water. You'd only run off about a gallon of wort with that. FWIW, I use a total of 9 gallons of water on average for a 5.5 gallon batch. I mash in a cooler and have minimal dead space. Usually I'm around 6 - 6.5 gallon of mash water. The rest to sparge. Depends on the recipe. After grain absorption, hop loss, boil off, and kettle/tun loss, I end up with about 5.5 gallons into the fermenter. Which usually allows for me to get a full 5 gallons of finished beer into the keg.
I did my first brew this weekend and I am not sure it was super successful.
I was following the recipe to calculate my strike water. the calculations came out to about 4 1/2 gallons of strike water. I put in 6 since I cannot empty my keggles 100% due to the location of the valve.
I also followed the suggestion of adding extra water to the mash until it was below the false bottom. (3 gallons). I mashed for an hour, per the recipe, then sparged.
By the end of sparging I had a little under 6 gallons in boil keggle. I did the boil then chilled the wort and added it to my primary. I ended up with about 3.5 to 4 gallons of wort in my primary. Per the recipe I added water to get it to 5 gallons.
I checked on my primary this morning and found no activity. Along with the water issues I also incorrectly read the temperature for the mash, so instead of 150F I was close to 180F. Also the liquid yeast I used had be left out for a day, then put back in the fridge, and pulled back out this weekend when I brewed.
So not the ideal start to my all grain brewing experience but I am learning what not to do.