Adapter is not not ready for pickup until the stunning will autodetect required information - thus it will not provoke users to pickup by ringing.
The STUN is just method of autodetection of some parameters of your environment. Assiming your environment doesn't change so much, it's superfluous to detect parameters again and again. Just configure adapter statically and turn stun off.
Please note my response is based on information you provided (and you didn't provided logs from ATA related to an affected call). If you provided incorrect/incomplete information my analysis may be wrong and delay may be caused by something else (CallerID transmission is more common cause for delay like this one).