In order to get in most efficiently you want to dive at just the right moment to get in while the ramp is still opening up. For multiplayer, players should line up 2 on each side. This works because the flaps on the side do not have collision, as you may have noticed when getting "stuck" while playing casually.
https://youtu.be/ic7DOcZ5w0o?t=164
Another method involves clipping into the flaps as they are opening up in order to get even closer to the cabin.
https://youtu.be/HoppKv4jYc8?t=190
If you leave the extraction zone right as you hear the words "Pelican-1 approaching pickup", but before the shuttle spawns in, Pelican-1 will hover shooting his autocannon at enemies in his line of sight until he runs out of ammo. Any Helldiver who re-enters the zone will cause him to land, and any reinforces can also sometimes force a landing even if the player steers out of the way.
Since ideally you will board the shuttle as fast as possible, most of the time you will have already fucked up the run when doing this in solo or multiplayer. However its a very powerful ability to use as a last resort or when playing casually.
https://www.youtube.com/watch?v=lios9A3rtPE
Note: guide is outdated, Pelican-1 is now invulnerable to damage