Without logistical hurdles: 8 Months Minimum
Basic Training: 8 Weeks. This provides the basic (minimal) set of soldier skills: Safe weapons handling and use, combat movement and reactions, communications, first aid, and fieldcraft. It also weeds out the unfit and identifies potential leaders.
Advanced Training: Another 8 weeks, though some specialties need much longer. This is where truck drivers learn to drive and convoy, infantrymen learn how to mesh their fighting tools as a team, clerks learn to type and how the forms work, artillerymen how to load/aim/fire their guns, etc.
Some skills take longer: Aircraft pilots, Intelligence Analysts, Medical Technicians, and many other skills need much more than 8 weeks of training if you want them to be effective. If you need effective sky jockeys who can survive, for example, then they become a limiting factor, and your minimum training time for the Army will be an additional four months or so.
Unit Training: Once individual skills are in place, the recruits are (re)organized from Generating Force training units into Operational Force fighting units, and the units begin collective training - how to operate and fight as their intended squads, platoons, companies, and battalions. There is no top limit on this time, more training results in better unit proficiency. I'm calling this four months, which is much less than the full year USA Regulars prepare for a typical deployment...but the question seems to imply that it's a bit of a rush-job. Honestly, longer would be better.
In real life, it's likely that there would be LOTS of logistical hurdles, and inevitable delays will stretch the real time longer. This timeline assumes that 100% of your trainees show up on Day 1 to fully-prepared training camps, which is quite unrealistic. Training camps don't build, stock, and train/man themselves overnight. Drill instructors are trained, not born. Strapping your tank onto a railcar or truck cannot be haphazard, or you will destroy the tank (and the bridge it ran into). Food, pay, corruption, boots, fuel, bedding, heat, transport, pilferage, cyclones, ammunition - so much can go wrong, cause delays...and certainly will go wrong when starting from scratch.
From start to finish realistically, plan on one full year to have your first new units armed, trained, and reasonably ready. Again, additional training time beyond that will mean additional combat proficiency.
In an emergency, you're tempted to reduce training time or scrimp on skills. You can...but ONLY if you have a thorough understanding of the enemy's likely behavior and capabilities. If you train your army for, say, counterinsurgency, then that's all they will be good at. When a neighboring country invades with Regulars instead, your ill-trained Army will fall apart. Senior leadership at the national level must manage (and prepare contingencies against) many such risks to the chosen strategy and the forces.