By default, the FAST search site template is missing.  It has to be enabled via PowerShell.  Luckily, this is a very simple process.

Perform the following steps to enable the template:

1. Login to one of the web front ends
2. Open the SharePoint Management Shell (PowerShell for SharePoint)
3. Type or Copy/Paste in the following making sure to change the “Identity” to your site collection:

$site = Get-SPSite -Identity https://nameofsite.com
$site.Features.Add("5EAC763D-FBF5-4d6f-A76B-EDED7DD7B0A5")

Your output should look like the below screenshot