It sounds like you're asking, "how do I find beta users or driver early adopters?"
As Frederic seems to suggest, you could "hire amateur sportsmen" and have them "organize local sports events" while using your social media network to do so.
There are plenty of different places (both digital and physical) were you could find enthusiasts who might likely be curious about the platform especially if there's a particular segment in sports you may be after (i.e. it may easier for you to have tennis players curious regarding a tennis specific social network than, say, a more open-ended/generic platform).
Additionally, I would say, there's an important factor in budget; are you able to offer upfront payment & contract to early testers/users as 'brand' or 'platform' ambassadors perhaps? are you able to create marketing materials that reach out professionally or are you wanting to have a more candid conversation in the hopes that you find beta testers who are interested in using the platform of their own accord? If you've got the budget, then outright hiring a few users who may be locally influential in their particular sport could be a good option, and reaching them directly via contact information they may have available online could work. If you're looking for more casual beta testers then it may be easier to approach an amateur team and try to drive adoption in their sport league.
It's still difficult to suggest a definitive approach without knowing much other than a social media platform for sports amateurs (is it for organizing events? leagues? tracking statistics for games/events? messaging between amateurs for pick-up games? is it for one sport? a group of sports? all sports? is it for younger athletes in traditional sports or casual 20-40 yr olds playing kickball on Saturdays?)
As a quick sidenote/example, there are several amateur leagues with several teams in my area that offer an opportunity for small time sponsorship; you can sponsor a team as an individual/company/etc. in these amateur leagues (ultimate frisbee, soccer, kickball, dodgeball, volleyball, softball, etc.) for as little as $150 a season; now, they have several sponsors and they use these funds for jerseys or events, etc. but most teams (even the more amateur ones) have a website or a social media site setup (facebook/meetup/etc.) with contact info on how to sponsor them. You could always sponsor an individual team simply to build awareness of the platform and reiterate through several sports leagues in the hopes that growing interest leads to early testers or you could more formally contact the teams and offer more than the $150 sponsorship level were the team to use your platform to setup practices/hangouts/etc.
Again, just my 2 cents!