How do I unlock a carrier-locked SIM without paying?

Apple has nothing to do with the carrier lock that might be placed by a carrier.

The carrier locked the phone. Only the carrier can unlock the phone.

Contact the carrier. If the carrier requires payment to unlock the phone, your only option will be to pay the carrier to unlock the phone.

No 3rd party can legally or effectively remove the carrier lock from a phone.

IF they manage to remove it, it is either by using a 'hack' which will render the device unsupportable and will be removed when it updates, or by using a 'man on the inside' to illegally remove the lock, which WILL be discovered at some point and the device will be re-locked.

ONLY the carrier it is locked to can remove the carrier lock. If you are not a current or former customer of the carrier it's locked to, odds are virtually non-existent that they will remove the lock for you.

Can Apple help me unlock it?

No, only the carrier it is locked to can unlock it. And if you currently don't have service with them, they may not unlock it for you.

How to unlock your iPhone for use with a different carrier

https://support.apple.com/en-us/HT201328

great40 wrote:

Please how do I unlock my sim without payments as I didn’t buy my phone directly from the carrier

Is it reasonable to infer, from this, that this is a second-hand iPhone?

If so, you may be lucky that the only issue you have encountered so far is carrier lock. Sometimes, second-hand phones turn out to be lost, stolen, or improperly prepared iPhones that turn into Activation-Locked "bricks".

The All Too Common SAD Reality of Buying a Used iPad/iPhone – Apple Community