Yes, but the there have been three different “Reds” in Cincinatti. The team that was a founding member of the NL disbanded. The third team didn’t join the NL until 1911.
The other remaining founding team is are the Braves.
I didn’t know that. I thought that traditionally the first regular season game was played in Cincinnati because it had the oldest National League team (and of course the NL is older than the AL).