When to start looking again?

I recently started a full-time swe job at a mid-size software company in my hometown. I interned 2x at the company and wasn't really planning on staying after I graduated but I didn't get any other offers this year (barely any interviews either). I don't want to be here for long and would like to move asap.

But how much breathing room should I give before applying to jobs? Does it look weird to start looking for new jobs the same month you started one?