I have a Yamaha 115 that does exactly this when going from neutral to forward. If I advance throttle slightly and then return to idle, the vibration goes away. I’m thinking it is the shift cable adjustment.

I looked at the linkage and found a video saying the two scribe lines, one on cam and the other on bracket should align at neutral. My cam was set forward about 3/8″, so I adjusted it back to align it. Tried it with the cups and hose and it seems it may be improved. Will know next time at lake.