For new(er) construction that's in the boundaries of The Woodlands…probably. Unfortunately, that's where we've been since early 2021.
There is 2300 sq ft 3/2.5 in my neighborhood that just listed for $595k. No pool.
There is a 3/3 that also just listed. It's a little bigger at 2600 sq ft, and it's $525k.
I have a 2/2 that's roughly the same square footage as the first house posted above and it would probably sell for $450k-$500.
$450k is the new $300-$350k, which was pretty much entry-level pricing pre-Covid (3/2, 2000-2500 sq ft). New construction has been higher than that, though, just because there isn't a lot of it in The Woodlands (most new construction is outside the boundaries).
If you find something, it's most likely going to be older/need a lot of work or have a major flaw (like backs up to Woodlands Parkway). Or both.
I'm not saying you won't find anything. Inventory at that price point is just really low right now (and has been for a while) and it might take some time. Other option would be to start looking on the east side of 45 or to the north towards Conroe.
Are your kids old enough for public school? If not, you may want to consider renting in the general area until prices come down and/or you find something. I actually know of a 3/2 rental that's almost ready for move in. It's zoned to Klein ISD, though, so if you have kids in school, I wouldn't recommend it.
Edited: I just did a quick search a saw a couple of options that fit your criteria (and aren't in a 55+ community - have to watch for that, too). At least one has been "reduced for a quick close". One is updated, but they are both 30+ year old homes.