So I have a question for mommas out there, I have a travel system stroller where the car seat pops…

So I have a question for mommas out there, I have a travel system stroller where the car seat pops into the stroller and there are two covers (one attached to the stroller and one attached to the car seat) so my baby boy would be completely covered. I'm planning on taking him to the boardwalk during the summer, he won't be getting too much sun exposure, I'll be in and out of restaurants and stores, and the sidewalk is partly covered from the sun, what are the best steps to take to make sure he stays cool and doesn't get too hot and doesn't get sunburned since he's gonna be too young for sunscreen, I'm gonna try to pump milk for the day too. Any advice?