Exact same thing happened to us, we bought a dummy but she didn't really take it, so we didn't persevere.

Normally A is fed to sleep, sometimes she goes down slightly awake and either nods off herself or crys out and I pick her up and pat her bum while she is over my shoulder and she drops off again.

She def prefers to suck and has recently found her hands.
But I also noticed that sometimes if I popped her back on the boob, she would have a big feed again, so was still hungry, but had just nodded off.
She also wanted to suck when she had tummy pain as it was a comfort thing, so I had to burp her well.

Not sure if any of this is helpful.

Congratulations on your bubba :$



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