No, we don’t necessarily need to fully solve the origin of life on Earth before we can remotely detect life elsewhere.

Remote detection (like with telescopes and space missions) mainly depends on identifying reliable biosignatures—signals that are strongly associated with life, such as:

Atmospheric gases in imbalance (e.g., oxygen + methane together)
Surface chemistry changes that are hard to explain abiotically
Potentially industrial pollutants in the future (technosignatures)

We already have enough understanding of Earth’s biology and chemistry to propose testable signatures of life, even if we don’t yet know exactly how life originally started here.

However, understanding the origin of life does help improve confidence and avoid false positives. For example, if we better understand how non-living processes can mimic biosignatures, we can design better detection methods.