My guess is you are sitting at a light, the car is out of gear and your foot off the clutch.
The light Turns green, you push the clutch in, and shift into first.
You hear a clunk noise and feel the shifter move.
This is normal
When your transmission is out of gear and your clutch is engaged, the input shaft of the tranny is spinning with your engine and flywheel. As @
Ultramaroon stated, the input shaft has enough rotating mass that it will continue to rotate for a short duration after your push the clutch in. That rotation will torque the synchro and gear when you select a gear and create a noise and feeling you described.
Now, if you push the clutch in and wait a couple of seconds (maybe 3) the input shaft will have stopped spinning and you won't get that anymore.
If you have driven hondas or other FWD vehicles in the past that have cable linkages or other longer/more complicated linkages, the play in the system may have isolated you from that noise and feeling before.