String manipulation

The worst. I promise. You essentially need to split your string at each . - Fortunately, Roblox has a function just for this purpose. Use string.split to produce an array of names.

input = input:split('.')

Then remove the leading game if it's there

if input[1] == 'game' then table.remove(input, 1) end

And finally walk through your array, getting each child along the way

place = game
for _, v in pairs(input) do
  place = place:FindFirstChild(v)
end

And place will be the Instance you referenced. Provided it's valid, of course. If it's not, then your script will error out. Catch this with pcall