Focusing on GRE, subject GRE, TOEFLS, IELTS before applying? Applying to the US:

I just finished my master's in mathematical finance. I want to apply for a PhD in math (but not in mathematical finance).

Can I start applying this year while studying and taking exams (GRE, subject GRE, IELTS, TOEFLS), or might my time be better spent on the latter?

I'm fluent in English, it's my only language, and I have a master's in math so I don't expect the GRE, IELTS or TOEFLS to be too difficult, but I may have to spend a lot of time studying for the Math GRE, which appears to be the equivalent of an LSAT/MCAT for master's or PhD and a bar exam/USMLE for bachelor's or master's.

What is the common practice in this matter? Do graduate school applicants first focus on studying and taking GRE, subject GRE, IELTS, TOEFLS, etc and then worry about applications after?

Suppose a graduate school applicant intends to study for one of those. On average how long does it take to study for, apply for, take one of those exams once (for the sake of example) and get the test (just one, for example) score?
For grad school, the GREs and TOEFL are treated more as thresholds. Once you cross the target score it may not have much of a bearing on your admission. For the general GRE, do some of the sample exams provided by ETS and see how far your score is from the prescribed targets. You can count on improving at about 5 points per week (so if you score 310 and your university needs 325, plan to study for three weeks). The TOEFL shouldn't be an issue for you based on your other Academia posts. The subject GRE requires at least 2 months of serious preparation. Again, try to see where you stand.

Try to do the exams at least a month before the application deadline, as that is how long it could take for the scores to reach their destination. If you are applying for a competitive program, you will need all your scores in place. Since it is only June, you have enough time to apply this year (to join next Fall).