This will sound counter-intuitive, but calling individuals to ask for small favours is a good way to build rapport and to learn more about your colleagues. Most people are very happy to help out the new guy, and asking a small favour is a good pretext for starting broader conversations about the topic they're an expert in or, even better, are passionate about.

For example: "Hey John, I'm spangry and I just started this week in team foo. So and so tells me that you're the resident expert on x. I'm planning to do some work related to x and figured, given I'm new and all, I should talk to you before starting. Have you got a moment to talk about x?" Then ask your favour and they will likely oblige. After you've thanked them, that's your opportunity to launch into a more general conversation where you show interest in their background or subject of interest (e.g. 'So how long have you been at [company] for? Got any tips for a new starter?' or 'I did a little research on x before calling and read that y is a big issue at the moment. Just curious, what's your take on y issue?')

It goes without saying that being genuinely interested and curious about them helps greatly. I think the above works because (1) most people want to help, and they remember what it was like to be new (2) it's respectful, even flattering, that you're coming to them for their expertise and (3) broadening the conversation (but still keeping it on safe ground) generates additional conversation paths and further opportunities for building rapport.

Lastly, asking for small favours (which are obliged) may actually make people like you more as a post-hoc rationalisation for why they did you the favour (this is known as the Ben Franklin effect: https://en.wikipedia.org/wiki/Ben_Franklin_effect).