Upgrading tank- help

I have a betta which I got spur of the moment about 2 months ago. He’s currently in a 3 gallon tank which is too small. I got a 5.5 gallon today and have started getting it ready. I used the filter media from the old tank and some QuickStart. How long do you think it’ll take to cycle? I’d like to get him in ASAP. The water in his current tank seems to have good parameters. (pics of test strips and current tank provided) Thank you!!