> experimental evidence that time travel was not possible
This is making a large assumption, of course, that time travelers had any interest in attending his party, or that they even would have heard about it.*
Exactly, there are numerous reasons other than it's not possible.
1.Time-travel will never become possible.
2.Time-travel becomes possible. Their time travel capabilities are inadequate to visit us.
3.Time-travel becomes possible. They do not wish to visit us.
4.Our archiving and preservation techniques are inadequate. Our message does not reach the future.
5.Time travel becomes possible. They are willing and able to travel to the past. Our archiving and preservation techniques are adequate. The message has not been accessed in its future database.
6. Time travel becomes possible. They are willing and able to travel to the past. Our archiving and preservation techniques are adequate. We are not able to perceive or become aware of their visitation.
7. Time travel becomes possible, however traveling back in time opens a new timeline and the old timeline exists in the past of the new timeline unchanged. So we observe the old version of the timeline, wile there's an alternate reality where guests attended the party and another future rebased on top of that history.
8. Time travel becomes possible. They are willing and able to travel to the past. Our archiving and preservation techniques are adequate. They aren't allowed to tell us they are from the future or meaningfully interact with us in ways which might change the timeline (temporal prime directive).
Also, rebasing the future makes me think of time travel as git history.
Imagine the merge requests and the fights inside them
this would be a very unlikely scenario where in our current timeline there are no time travelers but there are at least one in each new timeline. If that becomes true it might be the ultimate vacations/retirement plan, create a new timeline where you are the only timetraveler
I'm big on #2 and #3 myself. I'm willing to accept that there are windows of time they can travel to with little risk (timelines, people, events, etc.). Also, the idea that proving time travel is possible by visiting people in previous times would be potentially dangerous or impossible (any uncontrollable variables lead to disbelief of individual).
What if time travel is only possible once?
Imagine the multiverse. All possible histories. In a possible universe where time travel is invented it is used, using time travel alters the past. The past conditions are necessary for the invention of time travel.
Time travel when used immediately facilitates all the possible uses of itself and changes the past so much that it deletes itself.
You can use it, but in doing so you remove the conditions for creating time travel. You can use it once and then you and your entire timeline cease to exist.
In such conditions I might reserve the use of time travel for things like preventing an unlivable hellscape and not waste it on attending a party with balloons.
A time traveler probably would not want to risk exposure, as most governments would want to capture and torture him for information. An interesting question would be, could an event be set up that allows a time traveler to reveal himself while retaining some form of plausible deniability?
One idea would be to come up with a secret value, then put it in an envelope for a while. Later on, you'd open it and publish the result. If anyone shows up and knows the secret before you open the envelope: maybe they're a time traveler! But while this might be convincing to you, it wouldn't be terribly convincing to anyone else -- they would assume you shared the secret with the "time traveler."
And this is effectively what Hawking did: the secret is just the location of the party.
(Obviously this isn't foolproof. If a reliable government agency prepares the envelope and makes sure nobody opens it, they could convince themselves you're legitimate. Which is why you need to do this as a fun, unserious joke.)
ETA: Also, if you wanted to make sure the government didn't torture the plausibly-deniable "time traveler" anyway, you'd swear everyone to silence and spread the rumor that "nobody showed up." How would we ever know? ;)
Better : people have to Guess on day 1 a random value generated on day 2, and the winner would be awarded with a Big amont of money. Privacy granted. Lottery. Lottery IS a Time traveller detection device.
There's an analog to the film The Man From Earth where a similar claim tiptoes on the line of credibility and insanity, with the audience never truly knowing.
This is making a large assumption, of course, that time travelers had any interest in attending his party, or that they even would have heard about it.*
* I do not believe in time travel.