How do i make it so that the timer from the line 14 goes off only after a player has jumped?

Instead of using a Changed event on the Humanoid, use the Jumping event. We can also disable the Humanoid from jumping internally using SetStateEnabled.

This code snippet below should work, but if it doesn't please let me know. I've added a few conditions: do not start cooldown if the player cannot jump in the first place, and to stop changing the TextLabel when the player died. I disable the humanoid from jumping until it requests the jump.

local PlayerService = game:GetService("Players")
local Heartbeat = game:GetService("RunService").Heartbeat

--Player objects.
local Player = PlayerService.LocalPlayer
local Character = Player.Character or Player.CharacterAdded:Wait()
local Humanoid = Character:WaitForChild("Humanoid")

--Configurations.
local Cooldown = 3
local Debounce = false

--Other objects.
local TextLabel = script.Parent

local function JumpWithCooldown()
    --Check if the player is not on air.
    if not Debounce then
        Debounce = true
        Humanoid.Jump = true
		Heartbeat:Wait()
        --Disables the humanoid from jumping.
        Humanoid:SetStateEnabled(Enum.HumanoidStateType.Jumping, false)

        for i = Cooldown, 0, -1 do
            --We want this to stop printing when the humanoid dies.
            if Humanoid:GetState() == Enum.HumanoidStateType.Dead then
                TextLabel.Text = "You died. " .. i
                break
            end

            TextLabel.Text = "Jump cooldown: " .. i
            wait(1)
        end

        --Reenable jumping.
        Debounce = false
		Heartbeat:Wait()
        Humanoid:SetStateEnabled(Enum.HumanoidStateType.Jumping, true)
    end
end

Humanoid.Jumping:Connect(JumpWithCooldown)