Cold emailing (or DMing) to build your network is hard.
You're offering yourself (vs. a product or service), meaning you must be creative. Your cold outreach is more dependent than ever on thoughtful research.
You have to be authentic in why you're reaching out. Please don't ask to pick their brain about a topic. Literally cut the phrase "pick your brain" out of your vocabulary. Focus on something they're doing that's interesting to you.
Be specific.
Not sure what I mean? Here are a few bad examples from our DMs
"I'm reaching out because I'm interested in startups"
"I'd love to hear how you started Lavender."
"How have you thought about culture?"
People are busy. They don't have time for your under-researched questions.
Don't be offended if someone offers to spend time with you over DM, either. That's a win. They could have easily ignored you.
The truth is most questions can be answered digitally. Strike up a conversation. The conversation can lead to a longer phone call or an in-person meeting.
Also, if you want them to make an introduction... you have to build the connection first.