Outreach to clients with a solution that they need, BUT is not "top of mind" right now. What to do AFTER the cold call?

Lets say that you have a SAAS product that can save your clients money month on month. Now, you reach of out to them via cold calling. They talk to you. They understand what you have to offer. But, its not their biggest problem right now. Maybe they are not in "save money" mode. They are in "grow revenue" mode.

The issue is that you got them at the wrong time.

My Question: So, is it a good idea to add them to a email/messaging list? Is it a good idea to send them emails once a week? Just to remind them they you exist. The hope is that after some time, your solution will be "top of mind" for them. And hopefully, that day, your message will show up just as they are pondering what to do. And hopefully they will call back.

Does this make sense? How to you guys tackle the problem of "out reach at the wrong time"?