This chapter of the Call of Duty Cold War guide contains information on where to find ammunition and other weapons. Thanks to this, you will always be ready for a firefight because you will know how to replenish your equipment.
How to replenish ammo
There are 2 ways to replenish your equipment. In most cases, weapons dropped by defeated rivals are sufficient. Just step on the weapon to automatically get the ammo you need. Sometimes, however, this will not be enough and you will have to go for something bigger, e.g. an ammunition crate, as in the photo below. These crates come in several variants, some of them have grenades for exchange.
How to obtain another weapon
There are two ways to get weapons in Call of Duty Cold War. The first and the easiest way is to pick up the weapons of the enemies killed. They are usually of poorer quality (e.g. because of the lack of optics). However, sometimes the exchange is worth it, especially if the weapon you're equipped with at the beginning of the mission, e.g. a rifle, does not suit you.
Sometimes you can get other weapons just by looking around - sometimes they are just leaning against the wall and other crates, sometimes they lie on desks and tables in rooms. E.g. in Identity Crisis, in one of the memories, you can raise an SMG to get through the Vietnamese village more smoothly. Just look around, if you have a minute to spare.