Vehicle has to make at least one full orbit before deorbiting. Deliberate suborbital flights, even if they had the capability to go orbital (like the last Starship flight) don't count.
@JussiVilleHeiskanen Which reusable part of New Glenn will reach orbit? I believe the reusable parts will all be suborbital.
@dp9000 Ah, that's an interesting wrinkle - I wasn't aware that New Glenn wasn't shooting for orbit with their first mission. The spirit of the question is intended to be "which of these two programs will hit a common and easily comparable performance milestone first" and I think successfully achieving an interplanetary trajectory would be exceeding the requirements of achieving Earth orbit. I'm going to say yes here and change the question to "reach or exceed orbit" to account for this.
Good question!