Why didn't Jack Harmon simply enter the embassy basement by himself?

TLDR: Jack needed access to the circuity of the elevator to be able to upload Sarah's thumbprint and ID picture into the embassy's security system.

From the script:

JACK, wearing black coveralls and slightly odd-looking eyeglasses (they're called Visco glasses), enters an elevator shaft through a small door at the base of the wall. He looks up the shaft, shining a flashlight until he finds what he's looking for --

a gray metal box, protruding from the wall one floor up.

The party progresses a little bit more, and then the script states:

JACK climbs up the elevator shaft, towards the gray metal box. He just begins to remove the cover when he hears a noise from above. He looks up and sees the elevator above him descending.

JACK quickly pulls himself flush against the wall. The elevator comes down adjacent to him and stops, pinning him to the wall.

JACK Great. Come on.

Finally, a little later, the script states:

JACK is still pinned to the wall by the elevator, listening to their conversation.

PHELPS (O.S.) Jack's pinned down Sarah. Should be a second. Keep dancing.

ETHAN (O.S.) (with the Senator's southern accent) We were forced to tie him to my best stallion and drag him around the barn a few times.

Finally, the elevator moves down a floor and JACK is freed.

JACK Relax your crack, Foghorn, I'm workin' on it.

He quickly opens the gray metal box, revealing a maze of circuitry. He patches in his computer, climbs on top of the elevator, and hits the keyboard, beginning to download.

There's a split-screen of SARAH's thumbprint and the ID picture. JACK downloads her file into the security computer.

Ignoring the GUARD, SARAH turns and slides her thumb into the thumbprint analyzer once more. The panel glows, this time the message flashes --

IDENTITY CONFIRMED 

and the elevator doors slide open briskly.

So it wasn't just a case of opening and closing the elevator doors, but of ensuring Sarah could access the secure room by having her credentials uploaded to the embassy's security system.

Edit:

When the team are being brief, it is mentioned their objective is to photograph Golitsyn stealing the NOC list and apprehend him to his buyer.

Sarah and Ethan access the computer room where Golitsyn views the NOC list. In that room, Ethan leaves a pair of glasses which are used to spy on Golitsyn to discover the password he us using to access the NOC list. The only way they can discover that password is by physically going to the room and leaving the camera - and the implication through what we are told is this is only doable via entering the elevator and passing the embassy security staff.

We do see that Jim can open and close the elevator doors, so I understand the query about why not just enter the shaft, like Jack did, access the room and get out. However, the embassy could have security systems in place, such as CCTV, to enable them to easily detect intruders in the computer room. Instead, it was deemed safer to gain admittance via disguise.

I'll fully admit, my interpretation is pure conjecture (and the film is deliberately obscure in its opening film to create a sense of mystery and intrigue).