We present our lens mass model of SMACS J0723.3-7327, the first strong gravitational lens observed by the James Webb Space Telescope (JWST). We use data from the Hubble Space Telescope and the Multi Unit Spectroscopic Explorer (MUSE) to build our 'pre-JWST' lens model and then refine it with newly available JWST near-infrared imaging in our JWST model. To reproduce the positions of all multiple lensed images with good accuracy, the adopted mass parameterisation consists of one cluster-scale component, accounting mainly for the dark matter distribution, the galaxy cluster members, and an external shear component. The pre-JWST model has, as constraints, 19 multiple images from six background sources, of which four have secure spectroscopic redshift measurements from this work. The JWST model has more than twice the number of constraints: 30 additional multiple images from another 11 lensed sources. Both models can reproduce the multiple image positions very well, with a delta(rms) of 0 ''.39 and 0 ''.51 for the pre-JWST and JWST models, respectively. The total mass estimates within a radius of 128 kpc (roughly the Einstein radius) are 7.9(-0.2)(+0,3) x 10(13) M-circle dot and 8.7(-0.2)(+0.2) x 10(13) M-circle dot for the pre-JWST and JWST models, respectively. We predict with our mass models the redshifts of the newly detected JWST sources, which is crucial information, especially for systems without spectroscopic measurements, for further studies and follow-up observations. Interestingly, one family detected with JWST is found to be at a very high redshift, z > 7.5 (68% confidence level), and with one image that has a lensing magnification of vertical bar mu vertical bar = 9.5(-0.8)(+0.9), making it an interesting case for future studies. The lens models, including magnification maps and redshifts estimated from the model, are made publicly available, along with the full spectroscopic redshift catalogue from MUSE.