Personally I would open the nests.  When pullets first start laying they might drop their first eggs about anywhere, from the roosts or just walking around.  Most have control from the start but some don’t.  When a pullet lays her first controlled egg that becomes her nest.  If the nests are not open for that event you are forcing her to make her nest somewhere else so you have a habit to break.
Some people advise you to leave the nests locked up until they start to lay because they might possibly want to sleep in the nests.  They probably won’t but they might.  If they are going to sleep in the nests I want to know that before they start laying so I can fix the problem before I get poopy eggs if I can get them to lay in the nests to start with.
Often about a week before they start to lay they start looking for a good nest.  They might examine your nests and scratch around in there.  If they scratch the bedding and any fake eggs out you need to fix that before they start to lay.  That usually means you need to raise the lip on your nest.
Chickens normally like to lay where other chickens are laying so I use fake eggs to show them where a good place to lay is.  I use golf balls but others use ceramic or wooden eggs or plastic Easter eggs.  For bantams some people use ping pong balls.  How important that is was recently reinforced to me.  A snake ate the golf balls out of the nests and the hens started laying in a corner of the coop instead of the nests.  As soon as I put new golf balls in they moved back to the nests.  These were established hens, not pullets just starting to lay.
Even with everything perfect they still might not lay in the nests.  They are living animals and you just don’t know for sure how they will behave.  Their bird brains don’t always use the same logic we do.  They will look for a safe place to lay.  Hopefully that is your nests but it can be anywhere.  Even shadows on the coop floor might make a place look hidden and safe.  But by having the nest open and fake eggs in the nest you greatly improve your chances.
Straw works fine for nesting material.  People get hung up on what is “best”, but different people use straw, wood shavings, hay, carpet, cloth feed bags, Spanish moss, shredded paper (no newspaper, it stains the eggs), or many other things and are quite happy.  I cut and dry long pieces of grass around my fruit trees where I don’t weed eat or mow so I guess technically I use hay.  To me whatever you use should be readily available and in expensive.  You’ll find that people care about this a lot more than the chickens do.
Good luck!