If the initial estimate is close enough, it should take only a few updates (a few seconds) for AMCL to find a good match. You can trigger updates using a “localization dance”, like I mentioned above, or you can request “no motion” updates:
ros2 service call /request_nomotion_update std_srvs/srv/Empty {}
For example, in this video, I set an initial estimate using Rviz and then call /request_nomotion_update repeatedly until AMCL converges.
This works well when the initial estimate is close and the map has unique features for AMCL to match between the map and the laser scan. If the initial estimate was wrong and the room had repeating patterns (e.g. a perfect square room with 4 identical corners), AMCL would converge to the wrong pose estimate.
You could automate this with a node that listens to the /initialpose topic and calls the /request_nomotion_update service a handful of times in response.