Stargate: SG-1 series takes its name from SG-1 - the first of many teams USAF sends through the gate on a regular basis. The show focuses on that team, and in this way, it's similar to how Star Trek shows tend to focus on its eponymous ship/station. They somehow end up with most of the cool adventures and do most of the world-saving.
Where it feels more believable/acceptable than Star Trek is:
- SG-1 being special is at least somewhat justified. It's the first team Stargate Command sent through the gate (after the events of the original movie), so they got to be the first to make new friends and enemies.
- The show constantly reminds you about existence of increasing amount of other teams, through namedropping, discussing them, showing them, or showing multi-team missions. While SG-1 may be the tip of the spear, you know that SG-2 through SG-whocankeeptrack are following close behind.
- Unlike in Star Trek, in Stargate, humans start having no idea what they're doing. Quite often, it's them who need to be saved by more powerful forces, whether aliens or institutions.
Stargate: Atlantis starts with a focus on wider cast - so the gate missions are more fluid, you don't care much about who's assigned to which gate team on any given day. The whole ensemble of characters work similarly to a Star Trek series crew. But it makes sense for the same reason most of ST:Voyager made sense: Atlantis expedition is very far away from Earth, alone and with (at least initially) no backup.