One thing to note about the single player is that they really do want you to move around a lot. So while the ammo crates are there, they usually deeper in the fight. If you're like I was, and like to sit back in cover, you could find yourself running out of ammo quickly! Don't be afraid to get in there and mix it up.
Also, if you're speaking about the very first mission, I know I ran out of ammo right at the start myself, until I got my aim back and didn't waste ammo at the start and like I mentioned a moment ago pressed into the fight more and moved around.
The one thing to note is if you hang out next to it, shoot a few round and reload and accidentally get to close to the ammo box it will refill and use up one of the charges on the box. You could accidentally be taking up all your ammo when it's not needed. Make sure you're actually low to almost out of ammo before hitting those boxes again!