Best way to pre- finish plywood?

hi, I am making a 18mm plywood cabinet that I am going to paint. My previous experience with plywood is that no matter how well you sand the bare timber, after the first coat all these grooves appear that need to be filled



Can anyone please advise a good way of finishing so that I get a nice smooth glossy paint finish that doesn't look anything like plywood?



What do you recommend for finishing the plywood edges, as I use this timber for the drawer fronts too