I know for G2, you can get personalized links for folks to ask directly or add to email signatures. I did a challenge with customer success teams where we funded a G2 campaign to reward customers, and also incentivized CS with company swag credits. First CSM to get a review submitted, first to 5, and overall highest number during the campaign timeframe. The βfirstβ incentives help people get started. I also provided scripts and email templates to make it suuuuper easy, positioning it to their customers like an opportunity to share their experience and get rewarded. You'll want to be aware of the timing of your campaign so it doesn't conflict with CS team demands like end of year, end of quarter, annual planning, etc.
This approach prioritizes quantity over quality, so be aware and make tweaks as needed to shift the priority.