TL;DR Your map has a long way to go, but that's OK. Learn from your studies and do a test, balance the mind then get some rest.
I've checked out your VMF, and I can already tell that there's a lot of work to do. First off, as Stack had also observed, the top skybox brush was encompassing the entire map, instead of just the top.
Next, the skybox was just that, a box. Now, don't get me wrong, these sorts of skyboxes are useful during prototyping, but as you develop your map, I'd suggest using the skybox brushes around the perimeter of the map for a better seal.
Responding to your primary issue, I'm guessing that your spawn points are too close together. It might be a good idea to spread them out a little bit, so that each player has proper space to spawn.
Other observations include brushes clipping into each other, leaks, and certain world brushes with textures meant for displacements.
I know it's your first map but considering that all maps have issues on the first few compiles, it's okay to make mistakes, but the lesson to be learned here is if at first you don't succeed, experiment a few more times, and you might have something playable.
Still though, I admire your ambition to make your first map with the Payload game mode! Most starter mappers begin with test maps with either no objectives, or with the King of the Hill ruleset.
Keep experimenting, studying the Valve Developer Commentary, and testing map ideas! It doesn't matter if it's genius ways to assemble geometry, undiscovered use of entity logic chains, or gameplay ideas that only YOU could come up with.
One last word of advice, if there's a part of your map that you're stumped on how to fix, some downtime from map making can be helpful. Perhaps one of the more viable options is to sleep on it.
I'm serious, a good night's rest will let your brain combine multiple ideas, from whatever was on your mind before bed, to those that you've been unaware of. And after all that processing in rest mode, I bet you'll have a new plan to test on your new map.
