Physical mail through the postal service has no restrictions on who can send it. Anyone can write to an inmate via USPS regardless of whether they are on an approved email list, a phone list, or any other facility-managed contact list. Those approval processes apply to electronic messaging systems like JPay or CorrLinks and to phone calls, not to incoming postal mail.
This is an important distinction that a lot of people do not realize. The approved contact list controls who can send messages through the facility's digital platforms and who can call the inmate's phone account. It does not control who can put a stamp on an envelope and drop it in a mailbox. Postal mail is received and inspected by the facility's mailroom staff and distributed at mail call to the inmate it is addressed to, regardless of any prior relationship between the sender and the recipient.
So if you want to reach someone who does not know you are trying to contact them, a letter sent through USPS or through InmateAid's letter service is the way to do it. Write the letter, include the inmate's full legal name and ID number on the envelope along with the facility address, and it will go through the same mailroom inspection as any other piece of mail and be delivered to them.
InmateAid's letter service is particularly useful here because the return address on the envelope is InmateAid's address in Florida rather than your personal home address. That gives you a layer of privacy while still allowing the inmate to write back if they choose to.
There are no barriers between you and sending that first letter. Start there.