As far as I know, the only things you need to wait a bit before adding are muriatic acid and bleach together. Dont do it! One must be mixed through completely before adding the other.
I have a blue blob a little bigger than yours, and was swimming in it immediately. Arent you filling it with the same tap water that fills your bath tub...?
If I were you, I'd take the unopened chemicals back and go with the BBB method. It is quite simple and effective.
Step one, get a testing kit, no dip-strips! Test the water, and if you think you made a mistake, do it again to confirm, and write down the results. Since this is a "short term" pool for you, concentrate on Free Chlorine, PH and Total Alkalinity.
Step two, make sure your pool is filled to the fill line. The amount of water in your pool should be listed in the owners manual. Gotta know how much water is in there to know what adjustments are needed.
Step three, use the Pool Calculator
http://www.poolcalculator.com
Adjust the number of gallons at the top, at the bottom adjust the pool surface to vinyl, the suggested goals to TFP.com, and the chlorine source to bleach.
Enter the water testing numbers in the "Now" column and click "Calculate"
To the left of each field you will find the suggested chemical additions.
Wanna swim fast? Today?
After you get your chemicals {bleach, borax, baking soda} together. Assemble the youngun's in full swim attire. Tell the kids to get in the pool and form a choo-choo train going around the pool as quick as they can, dragging their hands in the water as they move. You are trying to make a whirlpool to mix the chemicals.
Pull the kids out, then add the chlorine first to the whirling water. This is the only chemical that might hurt, so do it first and just as soon as the kids clear the ladder. Pour gently from the measuring cup, you dont want to splash...never got it in the eye, but I do have a t-shirt with spots....Then add your borax and baking soda, sprinkling in the flow.
Wait 15 minutes, then add your kids and tell them to choo-choo train again! The bleach will be long dispersed by then, you'll be making sure the borax and baking soda granules are mixed in.
Then swim!
Water test daily in the late afternoon. Concentrate on Free Chlorine and Combined Chlorine. Free chlorine is the stuff that sanitizes your water. Combined chlorine is the result of chlorine finding something to sanitize, waste chlorine.
CC hits .5ppm, time to shock. Shock is a process, not a bag of chemicals {just use bleach}, read about it in Pool School.
The TA and PH should remain fairly consistent, and only require occasional slight adjustment.
I think you'll find a daily ritual of Test - Pool Calculator - Add X ounces of bleach - Swim. If your pool has a pump, pour your daily into the pump outflow and wait 15 minutes. If there is no pump, go choo-choo style, wait 15 minutes.
If you keep the pool up longer, you might think about adding CYA. This is found in pool stabilizer or conditioner, available at Walmart etc, contains cyanuric acid. Comes granular or liquid {wish I could find liquid!} Add the granular by pouring it into an old sock and hang it in the pump outflow, squeeze it often to help it disperse. This chemical will protect your chlorine from being burned off by sunlight. It requires occasional testing and adjustment.
If you dont get a test kit that test for all the chemicals, many pool stores will test for free. But, you gotta get a test kit and get into the daily 5 minute rountine, or you'll be GREEN before you know it!