You don't even have to stand close to someone to make contact. For example, you could make contact by telephone or by email.
What's more important is that making contact means to communicate with someone who you hadn't previously communicated with, or who you haven't communicated with for a considerable time, or when there was some barrier to communicating.
Let me improve my expalanation.
Literally, contact means physically touching something. But we also use it figuratively to talk about having a way of communicating with them even without touching them.
Being in contact with someone means having an established means of communicating with them, whether by phone, email, mail, carrier pigeon, meeting them at a certain pub on Friday afternoons, or whatever. Making contact means establishing this means of communication when it hadn't been established before, or if there's a possibility it's no longer effective. For example, by writing someone an email for the first time or by calling someone you haven't called in a long time.
How far apart you are does not matter when using this meaning of the word. You could be a physically touching each other, you could be on different planets, or anything in between, including "several feet away".
It could be anything from
Agent 9 spotted Agent 7 on the Moscow subway and made contact by standing next to her and tapping out a morse code message on her shoe.
The invention of the hyperspace laser in 2215 AD finally allowed humanity to make contact with the aliens of the Andromeda galaxy.