I personally chose to change all my cards near the same date (also around pay dates) so that when I pull a credit report I can have everything up to date. But I do have 4 cards that are due by the 20th and report on the 23rd which allows me to start using again on the 24. Whereas all but 1 other has a due date between the 24th and 28th and all report balance "as of" date or statement date by the end of the month.
I arranged the bulk of my cards to be paid the first week of the month then I have the rest around the middle. I pay whatever I need to pay on the bulk of them and then pay the minimum on the ones due later.
That way all are paid but the ones due later I can apply extra paymentss if needed. Works great so far.
I like my cards staggerd throughout the month..... and rotate which one I use depending on time of the month, size of the purchase etc.
I typically make several payments per month, so my "minimum" is always covered way, way in advance.... and usually make substantial additional payments prior to the statement cutting to keep the balance as low as possible or zero whenever possible.
If your second card is a few months old, I would apply for one more so that they age together, better to have three or more. If it wasn't in the middle of the covid 19 crisis where banks are "tightening up" I probably would say to apply for two on the same day ( I did )... and it worked out well... but others here may know better,