Boyfriend doesn't initiate much physical contact. What to do next?

Basically I asked a guy out and although he didn't really like me in that way (we've been friends for 3 years), he said he liked my personality and was open to trying. So we're dating. He'd always intiate conversations online and when I see him, he'd put his arm around my shoulder. But he doesn't really initiate much physical contact. So I initiated hand holding and I kissed him on the cheek at the end of our last date (and he would return it, though I'm not sure if it was out of obligation/convention/politeness). I initiated physical contact on these occasions because he saw me as a friend all along and I wanted to do something to allow him to consider me in a different way. So what to do next? Might be important to add we've only been on 2 dates. My plans are not to initiate physical touch for now, and just see if he'd do anything about it. Thoughts? We're both in our 20s but it's our first time dating someone.
Boyfriend doesn't initiate much physical contact. What to do next?
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