Train from Innsbruck to Venice

Where are you looking? There is indeed only one DIRECT train, but many earlier with connections. I see one at 9:24 with a connection at Verona Porta Nuova that will get you there by 2:40 pm. Or one at 6:22 with connections at Fortezza and Verona that will get you there by 11:40.

Some connections might not show up now, as they may be Italian regional trains. There is a system wide schedule change due June 8, and regional trains won't show until close to that date.

Which website are you looking at? I have been looking at so many, that I am not sure where the best website is to book train travel.
For my trip, I only need two trains. One from Munich to Innsbruck, then from Innsbruck to Venice.
Thanks for your help

www.bahn.com
You can't buy tickets there, because the trains are outside of Germany, but the schedules are there. Look at a date before June 8, the schedules don't change much, if at all.

Thank you. Where do I buy the tickets? How soon can I purchase them for July 15th

If you want the one direct train, which is operated by DB, then you can buy it through the link above. Or it will book an earlier leg just from Innsbruck to Verona, then you can go to Trenitalia.com to book Verona-Venice.

How soon, I know not. Right now, the 9:24 departure is for sale for June 3, but it is not showing for sale on June 10.
I am using https://www.trenitalia.com/tcom-en
That is Trenitalia, the Italian National Railway. You just have to keep checking.
Earlier departures will not show up until much later, possibly after June 1, as they are all regional trains. The good news is that they never sell out and are always the same low price.

There is a catch with Trenitalia ( https://www.trenitalia.com/tcom-en ). It only lists trains within, to or from Italy.
So it will list the direct train from Innsbruck to Venice (but you have to use the Italian spelling: Venezia). it will list the option changing at Verona, both trains are (at least partially) in Italy.
It would not list any option involving a change before the Italian border, because the first train is purely outside Italy and not in their database.

Conclusion: Only use Trenitalia to look up times for trips wholly within Italy. For times for trips crossing borders use DB ( https://www.bahn.com/en/view/index.shtml ).
Then when you have found your trains, use the website of the operator to buy tickets. In some cases you may need to split the purchase across two different companies' websites when neither covers the full trip.

The second catch is that when they change the timetable (December and June), Trenitalia often do not post the new times until a few weeks before changeover date.

As the trip originates in Austria, you buy your ticket at the website of the Austrian national rail carrier - OeBB.

https://www.oebb.at/en/

It is a bit tricky as OeBB's website does not show all possible connections with Italian local trains. When you have found a connection appealing to you using the time tables Sam had recommended, you may buy the Austrian leg from OeBB, and the next one from an Italian website.

Alternatively you could go by plane for $300.