How to determine whether I have an Atlas Pass

In order to obtain the Atlas Pass V1, you need to encounter a Space Anomaly. It will be extremely obvious when you've encountered one, as when you warp into a system with one in you'll see as you're exiting warp.

Inside an NPC will give a simple test for a milestone, then give you the blueprint for the Atlas Pass V1.

Once you've obtained that, you can start finding Atlas Pass V2 and V3. The fastest way to do this is to use a Bypass chip with one of the Orange beacons on a planet, and select 'Colonial Outpost'. Keep doing this until you get a waypoint for 'Manufacturing Building'. This type of building requires you to break down a door to enter. Solve the puzzle inside and you'll be awarded with a blueprint, which has a random chance of being an Atlas pass. The Atlas Pass V3 will allow you to enter V2 doors, so if you get the V3 before the V2 it's fine.

You do not get the Atlas Pass V1 from an Atlas Station, only Space Anomalys

The odds are actually pretty high that you will eventually "meet" somebody, as you can see. The odds of you being on the same planet at the same time and in the same place are where the odds drop like a rock unless you put in the effort and materials.

This is actually a version of the Birthday Paradox. With enough people involved the odds of two people having seen the same planet goes up VERY quickly.