For a civilian, the fastest way to the majors is probably the regionals (unless you pick one with a ten-year upgrade, but there are tradeoffs there too). But that does not mean it is necessarily the best way to the majors...

You can certainly go from corporate to 121 majors, and you might even have better QOL and pay along the way compared to the regional route. The challenges might be lack of 121 networking opportunities and lack of large aircraft experience. If you get into G-V/Global Express flying you should be good to go for the majors, but if you are a career citation, king air, or caravan driver that might be a hurdle.

Also some corporate operators are kind of shady...if you get violated because your employer is breaking the rules that might eliminate your shot at a major airline (as well as better corporate jobs). Unless you work for a real bottom-feeder regional, 121 employers do not usually set you up to fail with regards to the FARs.