If there was no custody or visitation order ever entered in Florida's family courts, then no court has yet exercised jurisdiction over these matters. Once a court does, in most cases this court will retain jurisdiction unless certain conditions are met.
When a family court has jurisdiction is a matter of state law. In Tennessee, state law specifically states the following regarding jurisdiction:
In order for a court to decide custody of your children, whether by agreement of the spouses or by decision of the court, that court must have jurisdiction.... [A] court of the state of Tennessee has jurisdiction to make an initial child custody determination only if:
(1) The state of Tennessee is the home state of the child on the date of the commencement of the proceeding... "Home state" means the state in which a child lived with a parent... for at least six consecutive months immediately before the commencement of a child custody proceeding....
(2) A court of another state does not have jurisdiction, or a court of the home state of the child has declined to exercise jurisdiction on the ground that the state of Tennessee is the more appropriate forum, and:
(A) The child and... at least one parent ha[s] a significant connection with this state other than mere physical presence; and
(B) Substantial evidence is available in this state concerning the child's care, protection, training, and personal relationships;
(3) All courts having jurisdiction have declined to exercise jurisdiction on the ground that a court of this state is the more appropriate forum to determine the custody of the child...; or
(4) No court of any other state would have jurisdiction.
At this point, the fact that you have not lived in Tennessee with the child for at least 6 months means that Florida will be the correct place to determine the custody issues unless the judge in the Florida family court agrees that custody should be decided in TN.
The fact that the father has filed a petition in a Florida family court seeking custody and these papers have been served on you does not constitute an exercise of the Florida's court's jurisdiction. So Florida has not yet exercised jurisdiction - no court has yet.
Remember that the courts and the laws involving custody, support, and visitation are completely silent on the issue of whether you and the father were ever married. This is not a consideration for making any of these decisions.
Florida follows the same rules (as do most states) when determining which state has jurisdiction. So in this case Florida clearly has jurisdiction to determine matters of custody, support, and visitation.
However, as the law states, the jurisdiction can be moved to TN IF the court in Florida decides not to exercise its jurisdiction.
What you are going to have to do if file a motion with the Florida court which has the custody papers and is planning to have a hearing asking that jurisdiction be declined to be replaced with the Tennessee family court.
Whether the Florida court is going to be willing to do this is ultimately up to the judge who hears your case. You need to ask the clerk when you call if there is a way to have the motion heard quickly, so that this decision can be made before the date of the custody hearing.
Unfortunately, unless Florida is willing to give up jurisdiction or the father is willing to withdraw his petition and file it in TN (hopefully just after you have resided there with your child for six months) you have no choice but to have the hearing in the court in Florida.
These laws establishing jurisdiction were created by the federal government and have now been enacted by most states, so that courts of different states do not try to exercise jurisdiction over the same child at the same time. Prior to 1997, things often became very complicated because the father would file for custody in the state in which he lived and the mother would file for custody in the state in which she lived (or had moved to) and two courts held two hearings with two orders (often different) regarding custody.
Now that these rules have been adopted by most states this rarely happens. However, people like you have gotten "stuck" as you have moved to TN without the father protesting, have been living there just under the 6 month requirement, but do plan on remaining there with the child. So while it seems logical that TN should have jurisdiction, the law makes it clear that Florida does.
Do call the Clerk in Florida and ask if you can have a motion heard by the judge asking Florida to give up its jurisdiction. (If the judge will hear the motion you can probably submit it in writing with your reasons for wanting the hearing moved to Tennessee, and the judge can rule without you ever having to move to Florida.)
If you cannot have the motion heard before the custody hearing, you can raise this issue at the beginning of the custody hearing.