IANAL but the answer appears to be no. Even an actual warrant doesn't count. Legal processing has to be required by the law of an EU member state, US court rulings don't count

See https://gdpr-info.eu/art-6-gdpr/ (6)(1)(c) (6)(3)(a/b) and https://gdpr-info.eu/art-48-gdpr/ (48)

That's not to say I know how a Google would react to a US warrant about an EU citizen (especially given the CLOUD act https://en.wikipedia.org/wiki/CLOUD_Act) but from what I can tell it's not permitted under GDPR