Do you think it’s possible for a man to love a woman but just not be naturally affectionate with her?

Its possible he expresses his affection in ways that she doesn't see. They speak different love languages.

Love languages: physical affection, spending time together, words of affirmation, gift giving, acts of service.
Ima mix of a lot of these. Which is common. I assume you know what your love language is, so his may be one that isn’t physical affection like spending time together or gift giving. It’s love, love isn’t always physical.