I'm pretty much the same. Nothing done before noon. I show up to the office on time just for the sake of it, I then get my work done at night. My manager is okay with it but it is not sustainable, I feel like it takes unnecessary time out of my day. But it is genuinely hard.
Can you negotiate with your manager about start time? I know it will depend on the exact team, but n my old team I would walk into the office at like 10:30 every day, and then stay in the office till about 7-8 every evening. I wasn't secretive about it, but nobody was upset, it was obvious that I was staying later to get work done.