Most stories involving time travel have it all wrong. They all want to go TO the future.
Isn't it just as valuable to get information FROM the future? About the future?
Given the best theoretical physics of our time, we can make assumptions about where our technology will be in like 1,000 years.
We can't build it today, but what should we be able to build in the future?
Thinking about stuff like dyson spheres and quantum entanglement.
Then, don't worry about sending a message...
Build sufficient technology to act as a receiver for a transmission from such technology in the future.
Then wait.
Like "Contact" and "Stargate" meets "Field of Dreams"...
Build it, and they will come. WE will come.