I mean, some people have less than that a month, you’ll be fine!
Get a spread sheet;
Food budget & make a meal plan (family of 3 and we’re around £150 a week on our food shop).
Budget for classes, there’s loads of free or cheap classes around. Bookbug - free and in twice a week at my local library, then a wee stay and play once a week for £2. Church hall baby and me class was £2/3 a week, baby sensory £10, swimming £15. Baby massage - £10.
Set a limit for coffee/ lunch out, I’d coffee maybe twice a week with other mums, then hubby and I would go for lunch at the weekend. Cafes are pretty reasonable & you can bring snacks for baby when they’re older.
Supermarket nappies are grand for during the day, but I’d always recommend pampers once little one starts sleeping longer stretches at night.
Jack & Jill sales/ market place/ aldi/ lild do fab baby toys (and they don’t need much anyway). Don’t feel obligated to buy loads of toys/ feeding accessories for little one, there’s so much unnecessary crap!