The right time is when the consultant knows enough about you to make an informed referral and your application timing is clear.

For many candidates that means after one or more useful conversations, not in the first message.

If you are applying soon, you can say so and ask for their advice on next steps, which gives them room to offer a referral naturally.

Do not wait so long that the application deadline passes just to make the relationship feel perfect. For more detail, see the consulting coffee chat guide.

tbh A short follow-up is fine. Repeated follow-ups started to feel awkward for me.

Alumni with a similar academic background were much easier for me to talk to than completely cold contacts.