A Cirrus jet pilot reported encountering Wind Shear on initial climb resulting in a temporary loss of control.

Narrative

A TFR was going into effect within minutes of our departure and I was determined to leave prior to its effective period. At the time of the incident; the wind was reported as XXX at 13. Peak gusts were over 20. In my experience; I thought the wind was well within my and the aircraft's capabilities. As we were cleared to depart runway XX; tower informed us that a Lear that had departed several minutes before us had reported LLWS on initial climb out. There are hills off the end of XX; and I gave little thought to the possible force of the rotors being created by the topography. After rotation; we retracted the gear at positive rate of climb and were immediately in moderate turbulence. This was forecast for our time of departure; but the intensity of the turbulence surprised us.Passing through 115 knots the flaps were retracted. Maintaining a stabilized climb was difficult and passing through approximately 400' AGL the autopilot was engaged. Almost immediately the aircraft entered an uncommanded roll to the left accompanied by a very strong updraft. We were restricted to 2;000' MSL; and the departure procedure required a turn to the right. As we quickly passed through our assigned altitude; I realized the autopilot had disengaged and had entered the ESP (electronic stability protection mode) mode and given the length of time of departure from normal operating limits; it then entered 'Level Mode' which was annunciated on the Garmin scoreboard. During these aggressively unusual attitudes; I was handed off from tower to departure. As I was able to check in; we experienced another shear moment; the bottom dropping out as we lost some 400'. The departure controller informed us that we were turned away from the assigned departure course. I believe they heard the fear in my voice as I tried to explain our flight conditions and they quickly coached us to help avoid an adjacent active TFR incursion. As our climb continued; the turbulence subsided and we were guided back on course and remained at our assigned altitudes without issue.So what did I learn from this experience? Although I have flown for decades through various areas of forecasted turbulence; it has never been during the takeoff and initial climb phases. Importantly; I didn't heed the warning of the proceeding departing Lear; which was overruled by my desire to leave prior to the TFR becoming effective. The Lear managed the LLWS far better than we did given its weight and speed. I should have returned to the FBO and waited for conditions to improve and the TFR to lift. The next mistake was transferring authority over to the autopilot. I just studied the two Pilatus PC-12 crashes from last year in which the autopilots disengaged in turbulence; and it appears the pilots were unprepared for the autopilots to uncouple. I made a similar mistake. I too was unprepared for the autopilot to uncouple; and; for ESP then Level modes to engage. I've read about these modes but had never experienced them in actual flight or a simulator. In reflection; I am surprised how long it took for me to understand the magnitude of the course and altitude variations from the expected departure procedure; and how long it took to process exactly what the automated systems were doing. Recognizing; processing; and responding; all took longer than I would have expected. Fortunately; I just focused on flying the airplane; getting it back to some semblance of straight and level; then given the gravity of variance from the expected course and the potential of penetrating the adjacent TFR veil (which did not occur) or traffic conflict; navigating and communicating. I am grateful that the departure controller realized the gravity of our situation and became a coach to provide the best outcome for all involved. I needed to integrate the new data (the Lear LLWS report) and override my plan on departing as expected. It was a variation of 'get home itis.' The result could have been very different.