noob mash question

So, I have only brewed 2 AG batches thus far and have so far had really low efficiency. I don't know yet if it is due to the grain milling at my LHBS not being fine enough or something else. Still working on that, but I did have a question. I have a 10g igloo cooler i use as a mash tun and I only brew 5g batches atm since I only have about 10g kettle. I was wondering as long as I can fit in MOST of my water into the mash, is there a reason I wouldn't want to and then just sparge with a small amount of water to just rinse any excess sugars out after? For instance like a gallon or gallon and a half? Anyways, maybe it's a dumb question but I just figured since the second runnings are a lot lower than the first if I would get better efficency doing it this way and just doing mainly one running then a small sparge.

Thanks, sorry if it's a stupid question but I didn't see anywhere about doing this or not doing this for any reason.

Actually you want to sparge with a lot of water to get a good rinse. Having a loose mash is fine for conversion but if you can't get a good rinse you'll have low efficiency because a lot of sugars get left behind. The no-sparge folks will give you a different opinion but if you are working off a recipe that expects you to sparge and you don't sparge well you're probably not getting great efficiency.

How bad is your current efficiency? How are your mash temperatures? How long are you stirring the mash when you add the mash water?

It is around 55-60%. Mash temps were correct throughout the hour I mashed (152). I stirred the mash for probably about 4-5 minutes or so to make sure all was stirred in. I did pour all the hot water in first then poured grains on top. I have heard that that is fine but I've also heard that that can shock the grains and make them not "work" as well doing it that way.
Any thoughts? Thanks!