In theory.

In practice, if I give you a random analog box, transforming it into an accurate DSP algorithm it's an extremely difficult problem.

Which is why people instead of doing that, they recreate the "idea" (reverb, delay, ...) digitally, but it's not a copy.

I've heard the recent Kemper Profiler uses advanced analysis to generate fairly convincing simulations of analog equipment, given its response to specially designed test signals. I haven't tested it myself though.

Although for some reasons 2021 was a great year for distortion/saturation plugins.

Any recommendations?

The hotly debated P42 https://www.pulsarmodular.com/product/p42-climax-line-amp/

The popular Kelvin Tone Shaper https://www.toneprojects.com/kelvin-tone-shaper.html

Maybe you want tape? London Acoustics Tapei https://www.londonacoustics.com/product/taipei-studio-tape-r...

As for freeware, the comeback of Variety of Sound with https://varietyofsound.wordpress.com/2021/11/30/tesslase-mki... or the less subtle https://kitplugins.com/pages/burier-free

This is just a part of (good) saturation plugins from 2021...

Not from 2021, but in May 2020 Fabfilter’s update to Saturn 2 is great, and the original was already a fantastic Saturation plugin I’ve used a lot.