Both drivers faced difficulties on track in Austin, with three incidents between the Silver Arrows in practice alone.
The W15 appeared tricky to control, with team-mates Hamilton and Russell both experiencing near-misses, spinning out on track before continuing the session safely.
Russell looked the stronger of the duo as the day progressed despite the older of the two British stars holding the record for the most wins at COTA, having secured five victories at the iconic track.
The return to Austin also presents the fourth sprint weekend of the 2024 season, with two more to follow at Sao Paulo and Lusail at the Qatar and Brazil grands prix this year.
Ahead of Saturday's sprint race, the FIA revealed changes had been made to Hamilton's Mercedes during parc ferme, a hot topic in Austin this weekend following a ruling that led to an immediate car change for Red Bull to prevent any chance that they may be altering their machinery under prohibited conditions.
A statement from the governing body read: "The following parts and parameters have been replaced / changed during the Parc Ferme yesterday and today before the start of the Sprint."
The document showed a part in the 39-year-old's car had been replaced with the approval of the FIA in accordance with Article 40.3 of the 2024 Formula One Sporting Regulations and therefore no punishment would be served.