Seems unlikely, but give it a try! You're right, the US starts with only 102 brigades.
But of course Mexico starts with only 16 brigades (4 CAV and 12 INF, all at pre-WWI infantry techs) and 1 INT (no ships). And just 19 base IC and 6.75 LS, but if you take Prepare for War and start raising threat on Guatemala from January 1, you can be at War Economy by May 1, with a whopping 23 effective IC, which is more than enough to build 5 INF divisions and 5 CAV divisions at a time. Your challenge is going to be neutrality. Prepare for War only lasts 300 days, and raising threat on Guatemala is a slow, slow process, so how to you even start a war before mid-1938?