According to NASA/JWST,

The James Webb Space Telescope (sometimes called JWST or Webb) is an orbiting infrared observatory that will complement and extend the discoveries of the Hubble Space Telescope, with longer wavelength coverage and greatly improved sensitivity. The longer wavelengths enable Webb to look much closer to the beginning of time and to hunt for the unobserved formation of the first galaxies, as well as to look inside dust clouds where stars and planetary systems are forming today.

But by necessity, the JWST won't do any of these things until it completes an unbelievably complicated sequence of separations, thruster burns, and mechanical deployments, involving well over 300 single-point-of-failure mechanisms; what the Goddard Space Flight Center website politely calls the "29 days on the edge," but most of the scientists know as the "30 days of terror."

Webb describes what will happen next if all goes well with this sequence:

At 33 days after launch we will turn on and operate the Fine Guidance Sensor, then NIRCam [Near Infrared Camera] and NIRSpec [Near InfraRed Spectrograph]. The first NIRCam image will be of a crowded star field to make sure that light gets through the telescope into the instruments. Since the primary mirror segments will not yet be aligned, the picture will still be out of focus. At 44 days after launch we will begin the process of adjusting the primary mirror segments, first identifying each mirror segment with its image of a star in the camera. We will also focus the secondary mirror.

By February 6, 2022, will the James Webb Space Telescope successfully see First Light?

This question will resolve positively if, before February 6, 2022 at 12:20 UTC, the James Webb Space Telescope has successfully turned on the NIRCam and captured any image, according to NASA