You wait for the portals to open and walk through them
jrstan is right, but that method isn't beginner friendly. So it's recommended just to go through the portal and do the map normally.
Wait for the portals to open Manage to somehow push yourself with a radio while being in a specific spot while saveloading. This should give you the saveglitch state, but as hat said, it's not beginner-friendly. Then, manage to grab the radio back and throw it below the vault, then move to the other side of the vault, then "hug" the radio, this should give you a "saveglitch boost" (some people call it "spd boost", though it's not SPD). Then get lucky enough to reach the elevator. Alternatively, you can do the "old" route with radio bsg that is hard enough as it is.
I would add that it is kind of like testchamber skip in HL1: it's hard, but it saves a shit ton of time so it's better to start WITHOUT it, then grind for it when you have enough experience.
An update has been released for SST that adds the command sst_portal_resetisg. This command removes Item Save Glitch and is to be used in place of restarting the game. This is a temporary solution while a more robust and legitimate one is developed.
The reasoning for allowing this is to make the ne