4 answers
It really depends on how fresh the breakup is and how you're handling it, to be honest. If you genuinely don't care and you can be around the two of them without it bothering you, then yeah, you can be her friend without any problems. The important thing is to be honest with yourself: if it's eating you up inside or you keep thinking about your ex, it's better to wait a bit before starting a friendship. At the end of the day people have the right to see each other, but your peace of mind comes first.
The reality is that if you can actually see her as her own person and not as "my ex's girlfriend," then it works! I've had friends who ended up dating people I knew, and the friendship lasted because I never saw it as an invasion of my personal space. The trick is not to fake it: if jealousy or resentment are still burning inside you, it's better to wait a bit before building a real friendship with her, otherwise it just becomes hidden tension.
The only thing that really matters is whether *you* can be okay with this situation without it becoming a burden. It's not a question of "can you" in some abstract sense, but of how you'll actually feel about it, day in and day out.
I had a similar experience a few years ago. An ex of mine started dating a girl who eventually became friends with a mutual friend of ours, and I inevitably ended up running into her in various contexts. At first I thought it would be weird, but honestly I never tried to be her friend - we were just civil when we saw each other. Then, over time, we discovered we had common interests and the friendship developed naturally, without ever being "forced" by anything. The difference was that I didn't go into it expecting to become her friend: she was just someone I'd see around. If I'd tried to build a friendship while feeling obligated to prove I was fine with everything, it would've had a completely different, more fake energy to it.
So here's my advice: don't decide "I want to be her friend" like it's some kind of challenge. Let it happen naturally if it's going to happen. If you actually like each other and your interests overlap, it'll grow on its own. If they don't overlap, it's nobody's fault - not every person we meet has to become a friend. And if you feel like her presence, or being around both of them together, is hurting you, you have no obligation to force anything.
What I'd do is stay away for at least a few months, just to give yourself some mental space and really figure out how you feel when you see them together. It's not that you can't be friends later, but rushing into it risks turning every moment with her into an occasion to think about him, and honestly it's not worth it. If down the line you find that you can actually see her for who she is without that filter of discomfort, then the situation becomes a lot easier to handle.
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