We like each other but is it a red flag that I'm the one to message him first most of the time?

It's a rare occasion for him to message me first, we recently confessed and I'm glad he likes me back but the fact he doesn't message me first a lot makes me wonder if he's just shy or nervous or if he just doesn't realise he should.. I've asked him about it before and he understood so he tried but it kinda died out to it being me most of the time again.
We like each other but is it a red flag that I'm the one to message him first most of the time?
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