The last time I had a new carb kit put in and the motor would crank and run fine on water ears but once I put the motor down into the water I couldn't get it to crank.
Unless you played with the timing rod it does not need to be touched. The only way timing goes out on an outboard motor is if something catastrophic happens and things get bent or you replace the stator. I would start with a compression test and a spark test.
What about the short rod to the magneto has that one been adjusted? If it was only the long rods you are fine and don't need to time it. Just a a link and sync