In section A, add echo/delay and increase feedback for a sound. When section A ends this sound has stopped playing but will echo into section B.

In section B the new sound or sounds may start underneath the echoes and this tends not to be so abrupt.

It's also I think good not to start everything at bar 8 or 16. Giving hints of a sound about to come in works too. If it's a five note riff, maybe earlier play one or two notes. Have this filtered and/or heavily reverbed or otherwise effected. Decrease the reverb when the sound kicks in for real.

Bouncing the sound that's about to come in, reversing it, and having that as a lead can work too. Try loading that reversed sound with reverb and echo.