Radicalization requires jostling. Personal jostling. Some people get there "on their own" by jostling themselves, but most require something that smacks them in the face.

Many of the impetuses that would do this are outside of our control, like losing their job, losing a loved one to privatized healthcare, seeing cops beat members of the press. For those cases, we can be loud and present and available to capitalize on their politically vulnerable state. Someone who wouldn't listen to anything you had to say about cops is suddenly ready to hear about defunding and abolition or maybe even the function of mass incarceration re: American capitalism.

The other is to do the jostling ourselves through agitation. To make the contradictions clear and obvious and to challenge them to reject the sociopathy implicit in their views that they usually cannot recognize. For example, I've had good luck radicalizing family members with frank discussions of the human consequences of imperial violence that's usually brushed under the rug. Some were mainstream libs that are now SocDems and some were SocDems that are now quasi-Marxist socialists that like Richard Wolff.

Other forms of agitation are also invaluable. Organizing boycott campaigns like BDS, organizing protests and sit-ins, presenting principled socialist candidates that know where to stick blame for the failures of liberalism, joining pickets, etc etc. It all helps.