American English has many casual phrases for making first contact.
Reach out. Contact someone, often for the first time.
Feel free to reach out. You are welcome to contact me.
I hope this email finds you well. A common polite first line of an email, often to someone you do not know well.
Ping me. Send me a short message.
Hop on a call. Talk by phone or video for a few minutes.
Shoot me an email. Write to me, quickly and informally.
Happy to connect. I accept your contact or introduction.