What he said ^ but more specifically, I stay in contact with a couple PT91 department heads that are in charge of 3-6 G550s depending on the department, and some lighter aircraft such as the Challenger 300. These departments use their Gulfstreams primarily for international long haul stuff - Europe, Asia, Australia, India, etc. and the smaller for their domestic needs. The bare minimum to have a shot with the Gulfstream shops is 3000 hours total time. Most of them also require an ATP, a PIC Jet type rating, and a Bachelors degree in whatever you want. Obviously if you have more flight time than that, you will be more qualified on paper - but to a lot of these shops, it's the attitude that matters more than the flight time. You can teach most folks how to fly, but you can't teach personality, work ethic, or dependability. Time in type helps for every shop I've talked to, and if you don't have that, then time in make helps as well (Gulfstream experience, Citation experience, etc.) They like to see 1000 hours of jet time, 1000 hours multi time, and 1000 hours PIC time. For the international big Falcon, Global, Gulfstream type shops - they want to see Atlantic crossings, CPDLC training (if your jet is equipped), international training, and a wide range of countries visited. To get this kind of experience, I would recommend going to the regionals for 1.5-2 years to build up a couple thousand hours - then transition to a Gulfstream flying PT135 company to get that international experience.
In my humble opinion, the most important piece of the corporate puzzle is NETWORKING. Most of these 91 departments hire people they know, because turnover at the good shops is rare and they want solid folks getting in the door. Get in there and start networking your ass off - be persistent, present a sharp image, and always have an updated resume with you. I've been stopping by one of the departments for 5 years and will continue to do so, because it's where I want to retire from. I wasn't anywhere near qualified for four of those years, but I've known them for a while now and I am getting within striking distance of their requirements.