Is it possible for my 1 month old to be teething?

Am I crazy to think this as I know it's very very early but I have this suspicion that my 6week old is teething recently. She's started to put her hands in her mouth and try eat her hands like crazy and this happens nearly all the time now - I know she's not hungry because she would have 140ml of milk and be completely content and full and then after she burped she would start with her hands, like I would offer more milk but she would not want it but still trying eat her hand. She also doesn't need a dummy to sooth as she's never needed it and can self-sooth very quickly. She also recently started to try chew on the teat of the bottle but she mainly wants to eat her hands than anything. Am I crazy or can this actually be a sign of teething? Or does she just like putting her hands in her mouth for no reason?