Air carrier pilot reported a NMAC during descent with a small aircraft directly ahead. Pilot made a rapid descent; avoiding the aircraft and reported that no TCAS alert or warning from ATC was received.

Narrative

I was asked to voluntarily submit a report with details for safety purposes; no proposed violation was involved. I've been flying for XX+ years with YY years active and reserve instructing/evaluating in military trainers. I'm somewhat of an expert at judging these distances and speeds. I changed the altitude in the FMS (earlier) at ZZZZZ to a hard 10;000 MSL from a range of 10;000-11;000 MSL as is typical for me. I was clearing both outside and inside to the PFD/ND to ensure compliance at ZZZZZ. At ZZZZZ +/- 0.5 miles (most likely at; or after); I noticed a red and white aircraft approximately 800 ft ahead; centered vertically in the Captains windscreen and 2/3 of the way across his windscreen towards the center divider. I was at a right 8-9 aspect angle (based on his aircraft) with an approximate 70 left heading crossing angle. His aircraft had near zero motion in the windscreen. In short I was flying up his 3-9 line; co-altitude with a 416 ft per second closure rate. Slightly faster if one considers TAS. Subtract from that closure rate the velocity they had in the same direction (near zero). I instinctively knew I would collide if I tried to turn right; or left. I most likely would have collided if I tried to climb over; but certainly would have sent him into an unusual attitude due to my wake/thrust turbulence. My only choice was to click off the autopilot; rip the throttles to idle and bunt under. I used enough force to miss the target; but with the secondary consideration of flight attendant and passenger safety. I would estimate this was a negative 0.25 to positive 0.25 G pushover. As I passed directly underneath; I became a little concerned that my tail might hit the aircraft. In short I had 2 to no more than 3 seconds to identify the threat and react appropriately. I could easily read the tail number across his fuselage; but wasn't concerned with that. At no time was there and RA; TA; or Proximity displayed on the TCAS. They apparently either didn't have the transponder; or have it turned on. ATCC did not have any reading; or skin paint of their aircraft on radar; so no warning was issued.Considering the size of the other aircraft; closure rate; and being nearly motionless in the windscreen; there was little room for any improved clearing technique on my behalf. A TCAS reading would have avoided the whole scenario.Suggest - Require transponder usage for all aircraft near Class B airspace; or their associated STARS and Departures.