Better to wait, and get a good pump.

You can maintain the pool without filtration -- so long as you don't swim, and add lots of 'people goo' to the pool -- by using bleach. I'd recommend Walmart's pool bleach, unless you have a better source. Use quart (4 cup) doses (4 ppm) added in the EVENING.

Also, you can use dichlor to add chlorine + stabilizer, since it dissolves very quickly. Each 1# bag of dichlor will add about 10 ppm of chlorine and 9 ppm of CYA (stabilizer). If possible, get the 24# box of dichlor sold by Sams Club. It's a good price and is (hopefully) local to you. Also, unlike almost any other dichlor available locally, it's PURE dichlor, and not mixed as a 4-n-1, 5-n-1, or 6-n-1 witch's brew. If you don't have a Sams, order the 24 x 1# In The Swim Chlorine bagged dichlor from Amazon.

Do you have a testkit? You need a good one. Strips don't count, though you can use them for now get an approximate pH reading and tell whether you have any chlorine present or not.

Get a HTH 6-Way Test Kit (~$23) (made by Taylor) from Amazon or Walmart . . . to start. Do NOT use the stabilizer / CYA test until AFTER you've added stabilizer. There are only 3x tests for CYA in that kit.

But, you'll almost certainly need the K2006 if you don't already have one.

Also, if you want to 'get it all' now, you'll also need refills for the CYA test: 16 oz bottle of R-0013 and Disposable plastic lab funnels. Try to order from Amazon rather than a 3rd party: Amazon handles shipping and warranties MUCH better.