maximum free iCloud Account

You get the ability to create additional accounts after 12 months. So if you created three (3) accounts on October 20, 2022 - come October 21, 2023, you should be able to create a new account once again. (I added a day for argument's sake)

Apple doesn't tell you, nor do I believe they have access to, when a particular Apple ID was created on a device. Say the last of the first three Apple ID's were created on October 18, 2021. You tried a week ago to create a new ID from this particular iPhone and got the rejection notice. (And rightfully so) Apple Support will tell you something along the lines of "you must wait a month" to try again. That's because they cannot tell you when the last Apple ID was created. Maybe it was 6 days ago. Maybe it was 11 months ago. Point is, it's futile to try every day.

Call Apple Support and explain your situation. Did you honestly buy the phone second hand from a site like eBay, Craigslist, or Swappa? Sellers don't have to disclose if they used the maximum number of free Apple ID slots to the potential buyer, so you could have been stuck with something that they either knowingly or unknowingly sold to you that you can't immediately create an Apple ID for. You might get approval for one more Apple ID, but you have to ask.

You're talking about Apple IDs. I'm talking about iCloud accounts. The error message the OP has encountered says 'The number of free iCloud accounts has been created on this device'. I've seen no evidence that this is time limited.

Maximum limit for creating Apple ID from the hardware address of iphone is three , you can't create more Apple ID accounts , however again sign in with your same Apple ID and it's account credentials ( in fact you have signed out the Apple ID ) in the empty fields or sign in with another apple id that was created from another Mac / iPad or different iPhone .

See the article Sign in with your Apple ID - Apple Support

I believe that Apple institutes a maximum number of free Apple ID's on a particular iPhone to three (3) per year. You can try reaching out to Apple Support over the phone; they will make sure that you don't already have multiple Apple ID's (based on your phone number and email address, device ID) and you might manage to get one additional activation slot over the course of that conversation.

Your mileage WILL vary, though. You can try creating a new Apple ID from the same iPhone by swapping SIM cards with a friend or family member. I am fairly certain you will find that it is restricted to the hardware ID and not necessarily the phone number associated with the account you are attempting to create. But it is one potential workaround that may not be openly suggested.

Source:

I had a [bad] habit of creating a new email address every couple of months. I would sign up for too many things with my personal iCloud email address that I didn't want in my mailbox and then I would be spammed to death. The first time I hit my maximum number (3), I was able to convince Apple Support to give me a fourth (4) by indicating I bought the phone off of Craigslist secondhand and was unaware of who had it before me. Whether they bought the story or have discretionary authority to make this change or not, I cannot say. I just know it worked for me.

Any one device can create only three iCloud accounts. This is tied to the hardware, is a permanent limitation, and there is no way round it. What you can do is to create a new iCloud account on another Mac or iOS device (not Windows or Android), then you will be able to sign into it on the device in question.