Create an arrival activity with a short round
If guests arrive from 6:30 through 7:15, start with something that resets quickly and can work at more than one player count. Tell arrivals where to put their belongings and when the longer game begins. Someone arriving five minutes before a round ends can settle in and join at the next break.
Decide whether the main game can start
For a four-player game at 7:30, ask who is physically present and ready, not just who said they would come. If three people are there, use a supported three-player setup or agree on another short round. Do not start with a fictional fourth player whose turns nobody can manage.
Offer a useful place for late arrivals
For example, play two short card rounds while waiting for dinner, then begin the planned team game after everyone has eaten. If a guest is much later than expected, ask whether to hold their place or adjust the teams instead of restarting every time the door opens.
A returning guest may prefer to learn by watching one round, join a team if the game permits it, or choose the next activity. Do not force everyone to restart a long game every time the door opens. Note which arrival arrangement worked and reuse it next time the group has uneven schedules.