There is no cause for concern. The Tesla Model Y's battery management system (BMS) manages the complete charging session from beginning ramp up to peak charging rate and then tapering down. The BMS will monitor the state of the battery throughout the charging session. Even if you don't precondition your Tesla Model Y for Supercharging before beginning a Supercharger charging session the BMS may perform some battery heating during the Supercharger charging session. This ensures optimal charging. Also, the BMS can access Tesla's charging history data that includes every Supercharger charging session performed on the battery pack in your Tesla vehicle. The BMS will not expose the battery pack to excessive charging rates that would stress the battery. At extreme low temperatures Supercharging charging can take some time to begin charging while the battery is being warmed, then charge at ~20kW charging rate (a small fraction of the maximum charging rate when Supercharging) for a time while gradually ramping up the charging rate. At lower battery pack temperatures the charging rate would never approach the maximum rate.