Both the OMC Cobra and Mercruiser A drive use Dog Clutch gear engagement.
Many outboards also use this type of gear engagement.
Going into gear is usually never an issue, it's coming from gear into Neutral that is the issue.
This is because of the Dog Clutch teeth inclined or ramped areas that hold them engaged once a load is placed on them.
This is part of the design.
Here's a Merc sliding sleeve.... very similar to the OMC Cobra.
While difficult to see in the image, the actual contact areas are inclined or ramped.... they are not straight or 90*!
Here are two of the corresponding speed gears and dog clutch inclined or ramped engagement teeth.
(the center gear is the "drive" gear.... or aka "pinion" gear by some people)
Example only in this next image:
Here we have the two "driven" gears (FWD and REV)
The "drive" gear is not shown.
What they're calling a "clutch dog" I'm calling a "sliding sleeve".
The sliding sleeve installs onto the prop shaft splines (splines are not visible in this image).
All hypoid gear teeth are continuously engaged with one another, and will be turning whenever the engine is running!
The sleeve is free to be moved in either direction for either gear selection.
Only the Dog Clutch teeth actually transfer power to the prop shaft when engaged with either the FWD or REV gear.
When in gear, and at low engine speed, and with the prop in the water, the prop thrust resistance places a light load on these engagement teeth.
Again... this is by design.
In order to over-come this load, we must momentarily lower engine RPM.
This is accomplished via the OMC ESA..... (electric shift assist).
Merc's system is a SA (shift assist).
The lower shift cable resistance moves/operates a cam lever that operates a micro switch during a change from IN GEAR to NEUTRAL.
The micro-switch (and it's circuitry) momentarily inhibits the ignition system.
During this quick ignition "stall", RPM is lowered, the Dog Clutch teeth pressure is reduced, and a shift can be completed simultaneously.
Once the shift is complete, engine RPM return to normal.
Your shift into and out of gear should be crisp, concise and with no hesitation.
If not, the engine may stall out and die.
It is also possible that the system is out of adjustment.
Or... the lower shift cable has become worn and is stiff.
What ever you do, or whoever you have correct and/or adjust this, the final testing must be performed in the water.
We cannot simulate the prop thrust unless the boat is in the water.
Good luck!