Arena 33 is correct regarding POSSIBLE time but "Why the big rush" a good question unless you are 40 plus. As you say getting the job at the end is the key but remember this is all down to the laws of supply & demand. CURRENTLY some exceptional students might be lucky to get an offer within a few days though this is very rare, more like months, occasionally years & for some NEVER.
The major ATOs usually have some job & career assistance links but this tends to be very informal, they are certainly not a pilot recruitment agency so don't hold your breath. In my view these links are over sold. In reality when the airlines are looking to recruit low-hour pilots they will approach the ATOs to see if they have any suitable candidates based on ground school, flying & MCC reports. In my experience this open to both integrated & modular students though most find jobs from their own efforts unless already 'sponsored' or 'tagged'.
Thoughts on degrees already made crystal clear. Does your budget for F/T ground school include accommodation & exam fees?