After taking a break, I realized I was approaching this from entirely the wrong angle. Instead of waiting for the module to initialize, I just need to wait for the variable I need to have data.

In case anyone needs to do a similar thing, this is what I solved it with:

private "_forcePool";
_faction = "BLU_F";
waitUntil {
	sleep 0.5;
	_forcePool = [ALIVE_globalForcePool, _faction] call ALIVE_fnc_hashGet;
	!isNil "_forcePool";
};

Either way, thanks for the help @SpyderBlack723

I'm trying to pull data from the globalForcePool, however I haven't found a way to wait for it finish grabbing data in a more robust way. I'm currently just sleeping for 30 seconds after mission start, which works, but I have no guarantee that this will work all the time.

I've tried waiting for waitUntil {!isNil "ALIVE_mil_OPCOM"}, but this happens before the globalForcePool is initalized.
Doing the same for ALIVE_mil_logistics never continues.
Doing the same for ALIVE_globalForcePool returns an empty array.

Looking into the code, it seems that the Military Logistics module has its own variables for startupComplete and initialAnalysisComplete, which looks like what I need, but I can't find a way to access those variables directly.

Any help would be appreciated.