How can I make a financial institution report my financial transactions to all the 3 major credit bureaus?

Usually, lenders report to one of the 3 major credit bureaus. You can request them to report to a particular credit bureau. You'll be in problem if lenders don't agree to report to at least one of the major credit bureaus. You'll make payments, but it won't help to build your credit.

You can request them, it is up to them whether or not they will accept it.

If your bank or lender doesn’t report a financial transaction (like a loan) to a particular credit bureau, unfortunately, you don't have any other way to force the creditor to initiate the process. Your financial information can only be reported to a credit bureau by your financial institution that subscribes to that bureau. Of course, you can always ask them to report to all three.

You can request them to report your transactions to your preferred credit bureau. It’s upto them whether or not they will keep your request.

Yes, you can't force. But you can always request.

There's no harm in asking. So, request them stating the reason, if required.
If you know that you have a good score on a specific credit report, you can always request your future creditor/lender to check that score, if possible. At least they will know that you have a good score, which means you're good at managing your financial situation.