Although telepathy the spell operates slightly differently, it's a good place to look for more info:
Until the spell ends, you and the target can instantaneously share words, images, sounds, and other sensory messages with one another through the link, and the target recognizes you as the creature it is communicating with. The spell enables a creature with an Intelligence score of at least 1 to understand the meaning of your words and take in the scope of any sensory messages you send to it.
I think the important detail is even though the communication is instantaneous, it doesn’t mean your wizard's response is. Have you ever had someone ask you a question, responded “what?”, and then within 2 seconds or so processed the question? That is basically the surprised creature's initial response in the first round.
Telepathy even if instantaneous is not appreciably faster than sound for short distances. Sound travels 100ft in 0.09 seconds. Nothing stops an unsurprised character from immediately calling out when there is danger. However, whether that can prevent others from being surprised is entirely up to the gm.
From the combat section of PHB
The DM determines who might be surprised.
Just as importantly is after a few lines.
Any character or monster that doesn't notice a threat is surprised at the start of the encounter.
Noticing a threat is different than being warned about that threat. So for me as a DM, warnings (by voice or telepathy) aren’t enough to avoid surprise unless they are made before initiative.