HADR Availability Group long sync time

I have the following problem / challenge: We operate an HA SQL cluster with several Availability Groups. In order to take full advantage of the load balancing, I redirect the SQL selects to the secondary host so that the primary is not additionally loaded. This also works flawlessly and super fast. BUT... If I do an INSERT, UPDATE or other dml out of an application and immediately after the result with a SELECT, the newly updated entry is not displayed correctly. My suspicion is that the replication on the secondary is simply too slow. Can it be because of the latency for hardening the log? How can I speed it up completely?