JWST doesn't measure in the wavelength range of the CMB, so I'm not sure what you heard but it doesn't sound right. Here are three things that might be related:

JWST needed about half a year from launch to the first science images. That time was spent unfolding the telescope (~1 month) and calibrating it and its instruments.

JWST can only observe targets in a ring around the Sun/Earth direction, in the worst case you need to wait almost half a year until your target is in view.

[Planck](https://en.wikipedia.org/wiki/Planck_(spacecraft)) needed ~9 month to make a full-sky map of the CMB in 2009-2010 based on the way it scanned the sky and again the issue that you cannot measure too close to the Sun.