I would argue that there is no such progression.
While push-hands may look like a "slowed down" version of sanshou, it is an entirely different exercise on its own.
The only way to progress to sanshou is to start doing it.
To elaborate, the practice of sanshou (or free form sparring if you like) is an integral (albeit rarely practiced) part of taijiquan as a martial system. It is ultimately, what all the other practices of the system are designed to support.
In order to progress to sanshou, the practitioner should have at least passing understanding of the core principles of taijiquan and have some experience in applying those principles. This is actually where push-hands comes into play.
You use push-hands practice, to teach how to apply core principles of taijiquan in a mildly uncooperative confrontational setting. It is not a hard prerequisite to sanshou however.
Below is my take on the progression to practicing sanshou.
Step 1: Single person drills
To start with sanshou, in addition to working on push-hands you should probably work on your fa jing (or releasing energy/power). In particular, learning to deliver your punches and kicks, first one at a time then in rapid successions - starting from a static stance and then adding stepping to the mix.
When feeling reasonably comfortable, try adding few more tricks to the game - first try adding some peng and lu for blocks and deflections and then slowly increase your arsenal.
Take care however not to get too fancy and complex. There is time and place for all the neat applications from the form, but this in not it. Most of the stuff you see in the form is rather advanced in the terms of practical applicability and usually works best if the relative difference in skills is heavily skewed in your favor.
At first I would not recommend to start off with hitting punching bags or dummies - learn to release fajing without using "external" (or muscular) force first and then use punching bags only for checking and improving the structural soundness of your punches and kicks. However, I've found that punching bags are useful for improving your punches, as they offer much needed focusing target and allow you to test the your fajing without fear of hurting anyone.
Step 2: Two person drills
You might want to start working on these at about the same time as you work on your single person drills. Maybe altering between two.
I would recommend starting out with relatively structured and well defined sets and slowly progressing to more free-form variants as your skill and confidence improves.
Probably the simplest thing to start with would be to try and apply lu and peng against a punch. Lu (or rollback) works the best against relatively straight punches and peng would work the best against hooks from outside.
Start out with one and first just learn the body mechanics of these techniques by starting out with low energy punches from one side, increasing the energy and speed of the punches as you progress.
Keep in mind that you are practicing taijiquan, not brawling, so work hard on applying proper body mechanics and core principles.
Remember the classics :
The jing [intrinsic strength] should be
rooted in the feet,
generated from the legs,
controlled by the waist, and
manifested through the fingers.
That means you should diligently work on using your entire body instead of only hands to deflect or block, which is the most common mistake.
As you get hand on the lu and peng, the one who feeds should start varying the right and left punches more often and varying the speed and adding occasional feigns to the mix, to make it more interesting and keep the duifang alert.
Also - at some point you should add stepping. First simple forward and backward half-stepping and then more complex sideways, diagonal and snake-stepping.
The main thing is - you should keep your drills alive.
One good exercise at this point is a variant of "willow bends", where you essentially just let your duifang attack you with various punches and your only concern should be to avoid those punches (and/or kicks) by turning your waist and using stepping - keeping yourself "just in range".
Use your imagination, but keep it real. The one that feeds, needs to feed punches and kicks, not caricatures of punches and kicks. They need not be delivered with full force, but they have to target the specific points on duifang. If duifang fails to void or block, they must hit the target.
Step 3: Freeplay
While at some point the drill may look a lot like freeplay, the important distinction here is that in drills usually there is an asymmetry of initiative, that is designed into the drill.
The most important thing in freeplay (ie sanshou) is that both of the duifangs have equal freedom of initiative.
You may intentionally limit various aspects of freeplay for the purposes of training. Usually it means limiting the "energy level" or intensity of the play, but sometimes you may also agree to exclude some techniques or distances to make it easier to concentrate on specific areas of your skill set - for example only limiting yourself to punches so that you would not have to think of dealing with feet while you are still struggling to handling the punches. Or disallowing take-downs if the conditions in the practice area make it either dangerous or impractical.
Start out with low intensity (10% is good) and work yourself up as you progress.