A solid-state solution would eliminate all arcing: turn-off and turn-on. You can either drive the solenoid with a solid-state relay (some already have clamping/protection diodes already built into the module as part of the package). Or, you can achieve similar results with a cheap transistor, base resistor, and a discreetdiscrete rectifier for the generated EMF.
The advantage of the SSR module is that it's a complete turn-key solution. You also get the added benefit of galvanic isolation in most modules. This solution is relatively expensive.
The transistor solution is cheap, but it's a DIY approach - basically you are making your own solenoid driver at this point. Adding your own isolation adds complexity if needed.
To answer your question, you are going to need to add impedance in series with the solenoid - some amount/combo of series inductance or series resistance to minimize the "pull-in arc". Or, switch the relay to a faster "quench the arc real fast" version or an oversized contactor so the arcing won't matter much.
