What I did this year when filling/opening my small Intex pool was add a quart of bleach to the pool after I had about 4" of water in it. At half full, as I could now reach for testing, I added enough bleach to bring FC level to a reasonable level.

When full, I put a trichlor tab in the skimmer basket. This dissolved the tab fairly quickly. It took about a week of 1-2 tabs at a time in the skimmer (pump running 24/7) to bring CYA up to 30-40, without FC going too high.

I've never seen the floaters work well as far as dissolving the tabs, those seem to be mainly for maintaining FC. Do be careful about using the floater during the season, as tabs will add CYA.

Side note to others who might remember my having built a wood fired heater last year: I filled my pool through the heater, and had almost swimmable temperature water when the pool finished filling.