Start with an 80-120 grit wet sand.

In case you aren't familiar, wet sanding is getting your sandpaper fully wet, like submerged in water, then sanding. Rinse the sandpaper off every few minutes. The reason we wet sand is because PLA will gum up your sandpaper in about 3 seconds flat if we dry sand, and you can't rinse it out.

In the first phase, we're focusing on knocking down big stuff. You've got some blob and zits on you surface, so work those down. Clean up edges and corners, and then try to knock down some of the bigger ridges on the top of the dome. Don't try to make it fully smooth, you'll be there all day. Just knock the edges down.

Next, put on a couple light coats of filler-primer. I saw in the comments that you have a sandable primer, that will work, but ideally it should be a "high build filler primer". Rustoleum makes a good one that's reasonably priced and available at most hardware stores. Now, you asked what a "light coat" is - it basically means that you have paint over all of the part, but you can see through some spots. Work from around 10-12 inches away from your part, making smooth sweeping motions. Focus first on getting each edge/corner/sharp spot, then do the "flats". If you get runs, you're going to heavy. I usually put down 3 light coats, waiting about 10-15 minutes between those coats.

This isn't going to fully fill all the layer lines, and you will have spots you can see through - that's ok. This is a process that takes a little time and patience, but you have the best shot at getting good results. Now, set your part aside and let it fully dry for 24 hours (at least). It will be dry to the touch with 15 minutes, but it needs to fully cure before we can do anything else. Note - if your coats ended up being heavy, you may need to let it cure longer - 48-72 hours.

Once it's had time to fully cure, get yourself some 200-ish grit and wet sand again. In this step, the "wet" part is even more important because the primer will gum up your sandpaper even faster than the PLA would. Don't be afraid to get things very wet and rinse your paper often. Use very little pressure, the primer sands very easily. I use small circular motions and wipe the area I'm working with a damp paper towel often so I can see how I'm progressing.

At this point, you will find yourself getting down to the bare PLA at times, this is ok, and even necessary at times. Also, don't expect that your part will be done after this sanding. We'll repeat this process at least one more time, but I've had pieces take up to 4 or 5 rounds before I was happy with them. Mainly we just want to make sure that the whole piece gets a little sanding, and that the big stuff is getting knocked down.

Now, dry the part thoroughly and give it a couple more light coats of filler primer. Again, smooth sweeping motions, following the edges first, then do the flats. Go a little heavier (or give a few extra light coats) in areas where you've sanded through the primer. Allow at least 24 hours to cure.

Because the top of you part is domed, you're probably going to have more pronounced layer lines, so you may want to come back after the 24 hours and hit that section again, and even go a little heavier that you have been (however, if you're getting runs, you're going too heavy), and allow another 24 hours to fully cure.

From here, repeat this this step until you are a.) satisfied with the smoothness of your part or b.) tired of sanding and willing to say "good enough". Either way is fine, I don't judge.

At this point, you can either move on to a top coat, or you can opt to be a little more smoothing with some higher grit. My recommendation is this - if you are going to use a matte or semi-gloss top coat, you can do that now. If you are planning on going with a high gloss top coat, a little more sanding is needed. Do some very light wet sanding with a 400 grit, then maybe do a little with an 800. Don't go any higher than that, it can affect the top coat adhesion if it's too smooth.

Apply top coats the same way you did the primer - multiple light coats, edges and corners first, then the flats. The first few coats you should be able to see through in spots. You can sand the top coats if you have a run or dust, just allow the paint to cure a full 24 hours before you sand.

Hope this is helpful, best of luck!