This is how I put my own Sims into a new save. Start the new game, which takes you right into CAS. From CAS, click on the Gallery, then My Library. Select your Sim to REPLACE the default Sim in CAS. Voila. Do whatever tweaks you wanted to do, and/or add Sims to this group. Hit the check mark as always and place them onto the lot of choice.
This Sim you have previously downloaded should have been saved to your My Library. Anytime you click the check mark at the start of a game it says something about this will save your Sim or words to that effect. Go into CAS and then select Gallery to see if that Sim is available.
