How often should a man take initiative in the beginning of a relationship? When to let the woman do the chasing?

New2this2
We’ve been hanging out about once a week and this week New Years Eve and Day together, I did some post contact initiation to see how she’s doing cuz she felt sick. After a few brief texts I let it be. It’s been a few days with no contact except today which she Snapchated me a pic of her dog and I responded with my dog. But nothing else. I don’t really consider that “making contact”. I really don’t know if she wants me to reach out to her, but I do enjoy when she asks me what I’m up to, and then I make a plan. Should I initiate contact over the next day to check her availability or should I let her come to me first then initiate the next hangout?
How often should a man take initiative in the beginning of a relationship? When to let the woman do the chasing?
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