Let’s assume your vinyl rig is at least B+ quality or higher (TT, arm, cartridge all pretty good)--and it’s optimally set up--and if it’s a moving coil or low-output moving iron cart, the step-up device is also at least B+ quality. That’s a lot of assumptions, complexity being one of the unavoidable facts of life of good vinyl.
Can you make digital sound more like that? A very qualified YES. Qualified because no digital device will ever match the slightly phasey vinyl sound, complete with surface noise (from imperfect channel separation, boulder being dragged through grooves, etc). But you actually can push digital to be somewhat warmer, more spacious, and more satisfying tonally & timbrally. Easiest way is to get a well designed/constructed NOS (non-oversampling) DAC. A well designed/constructed multibit DAC will probably suffice, too.
My NOS DAC is MHDT Labs Orchid, which includes a tube buffer circuit (I swapped the stock tube for a recommended new-old-stock tube). I no longer hear any of the digital nasties I thought were baked into digital back in the days I had delta-sigma DACs.
In all fairness, there are any number of overbuilt, uber expensive delta-sigma DACs that people rave about as being highly musical and un-digital in sound. I just can’t see spending >$15K to get to more or less the same more-like-analog place my $1,100 NOS DAC does.