One cause of difficulty engaging first gear is the clutch not disengaging fully when you press down on the pedal. You could check the following
Make sure there is no loose mats etc preventing the clutch pedal fully depressing ,,especially near where the pedal hinges.
Check the fluid clutch fluid level is correct. I think the Jazz has a combined fluid reservoir serving both the clutch and the brakes (If fluid level drops the clutch will fail first ,before it gets low enough to affect the brakes) Although fluid level can drop a little bit due to brake pads wearing down, any significant drop may indicate a leak in the clutch or brake hydraulic systems. In which case both systems should be checked for leaks, dont just keep topping up fluid. .
There may be air bubbles in the clutch hydraulic system, which needs bleeding out. This may be the cause if initially you have difficulty selecting first gear, but it becomes easier after you have rapidly 'pumped' the pedal to the floor a couple of times.
But there may be other causes other than the clutch. It may be a good idea getting the car double checked by a trusted expert before making any expensive clutch repairs.
But bear in mind if it is necessary to replace the clutch hydraulic slave cylinder and this requires separating the engine and gearbox its generally regarded as good workshop practice to take the opportunity of replacing the whole clutch as most of the work is already done .. - even if its not obviously worn out. And equally if a clutch needs replacing its may be good idea to replace the slave cylinder at the same time, even if not yet leaking. You can refuse, but dont assume they were trying to con you into unnecessary extra work.
