You can appeal it. Just be aware you are appealing the entire case so although it’s rare, it could result in a denial.
Thanks for elaborating on that.
I didn't like my onset date either, but the onus of that was on me. I didn't submit an appeal on time so I lost about 3 years of retroactive backpay through a partially favorable decision. The Administrative Law Judge (ALJ) wanted to connect my case, but he legally couldn't and explained why. I am grateful that he approved my case, and even more that he tried to go beyond for me.
But after the ALJ's explanation, there was no way I was going to appeal it.
Personally, I would take the win. However, I don't have a full picture to assess whether it's worth the risk to take on your part.