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I don't see why not. Your score suggests nothing negative present, solid utilization, etc. 1 year of credit history is usually sufficient to obtain credit from most lenders. Synchrony isn't particularly tough. The one piece of information that is crucial that you didn't mention however is what your income is. As long as it's decent, I see no reason for denial.
With a score of 800 I don't see why they would even bat an eye. My dentist office applied for me at the office and I was approved for a very small limit of $800 but this was almost a year ago when my score was in the high 500s with multiple derogs. I still have the Care Credit, haven't used it. But plan on using it soon. I asked for a CLI a couple months ago and was declined. I guess maybe because I haven't used it, or my credit report, or both. My score has improved alot since I applied. So I don't know. But I don't think they're super strict. And to answer your question, I never had to submit proof of income. Not to say that they would never ask for proof, but I was never asked and I don't make that much. In the $20,000s.
You probably won't be asked to prove your number, but don't lie because you might be asked, however unlikely, and it's a crime (fraud) if you are found to have lied.
However, be sure to check for recent changes in what you may count as income. For one example, if you are married or partnered, sharing a household, and you have reasonable access to all of the family income, you may claim the whole income as yours, not just your slice of it. If you are a student, grants and scholarships count.
Google for details that pertain to your situation, and good luck with everything!