Treat it like joining a new web forum community back in the earlier days of the internet. Follow and as appropriate participate in the on-topic sections (e.g. project-related slack channels). Lurk a bit in the off-topic sections (e.g. slack #random channel, but also look for others employees may have set up like #cooking) to get the general vibe of the place. Then make an effort to ramp up participation over time to a comfortable and, importantly, consistent level. As much as you're getting to know your coworkers, you want them to get to know and remember you, and all they have to do that is your regular participation.
Make an effort to connect with coworkers in person whenever there's a business or on-site trip. See if the company has any hosted events, holiday parties, or other in-person meetups (and if not, suggest some). If there's any coworkers that live nearby, suggest meeting up for lunch or after-work drinks occasionally.
Beyond that, as others have mentioned, you can seek out local social organizations and clubs, or even just try to interact with your neighbors more.