Even on an airtight saxophone the low C#, C, B, and Bb are challenging for the beginning player---especially at softer dynamic levels. These note require more air and are require the correct "voicing". Basically "voicing" refers to the shape and volume inside the oral cavity.
I teach inexperienced players to approach the low notes by playing a low G with a big, full, sound and then slurring quickly down to low C. It helps to sing those pitches on an "AHH" and mimic that feeling in the mouth and throat when playing the saxophone. "The lower you go, the harder you blow" is another tip I give them. When the low C is achieved, they then slur down and hold the low C as a long tone again and again to learn the "taste" of that note. From there they can either move on to slurring down to low B, then Bb using the same process, or work on coming in on the low C without having to slur down to it.
It takes practice at first, but once the "feel" of the low notes is achieved playing, those notes in a musical context becomes possible. In all the studies I have read where acoustic scientists use an "artificial embouchure" to play a saxophone in their tests, the "machine" usually can play only down to a low F or low E This shows how extremely important the "nuances" human beings must learn to master the low register on conical woodwinds.