If it's within a month- I'd avoid but thats just me being theoretical. I've never dated a woman even short term that wasn't relaying from last to next and consider that a foregone conclusion.
On the other hand, most guys I know, myself included are single for a period of time before starting another. Even then there is a good month or two of consistent companionship (feeling out period) before deciding on exclusivity.
Thats why I consider trying to lock it down too quick a red flag. It's needy and possibly deceptive. Lots of single guys cheat on their wives and S.O.s