Is it normal to want to marry someone after a month?
Depends.It depends
Yes, it can be normal to feel ready to marry someone after a month, especially when a new relationship feels intense. The feeling can be real without meaning you need to make a lifelong decision right away.
New love can turn the volume way up: you may feel unusually close, excited, and sure this is your person. Plenty of people have the “I could marry them” feeling early on, though not everyone would act on it so soon.
It’s fine to enjoy the feeling while giving the relationship time to show you how you handle disagreements, stress, and ordinary life together. Wanting marriage is one thing; rushing into a wedding is another. You can talk about the future without needing to set a date yet.