Flying out of Trieste to US

Looks like best bet is American with 2 changes, in Rome and DFW. If you take a train to Venice, you can do it with one stop in Atlanta on Delta.

I would start with the carrier you prefer to fly, see if they have a partner that services Trieste. My guess is that are few or no direct flights between OKC and Europe, or Trieste and the US; so you are likely looking at flying to someplace in Europe, then to a US gateway, then to OKC.

An alternative might be to look at Venice, there are a few direct flights to the US from there, but I would only take that option if a US destination has a direct connecting flight to OKC.

Search flights from Venice VCE, an intercontinental airport with non stop flights to the US. You can reach VCE airport from Trieste by train (train station: VENEZIA MESTRE) in about 2 hours. Just spend the last night near the airport since flights to North America depart in the morning.
www.trenitalia.com

I think Sam listed the 2 best options.

Depending on your specific flight choices, flying from Venice could be a few hundred bucks less than from Trieste, but offset somewhat by the cost to get from Trieste to Venice.

Flying from Trieste involves one extra airport to traverse, vs. making one extra hotel change to fly from Venice, and save a few bucks.
Really just a personal preference choice of which kind of 'extra' transfer you want to deal with.

Flying from Trieste has some additional considerations.

The airport is not near the city center, it’s at Ronchi dei Legionari. However it has a train station and therefore it can be reached from the Trieste central station in about 30 min. The very first train can get you to the airport just a bit before 5am.

The only way to make it Stateside on the same day is to fly ITA airways to Rome FCO and then take a ITA Airways/Delta (both partners at the moment) flight to JFK or ATL. JFK is not that good for you since there are currently no flights from JFK to OKC, so ATL is the only viable option. The ITA flight currently departs from TRS at 6:35 and arrives at FCO at 7:45. That should be enough to catch the flight to ATL at 10:15 (operated by Delta in codeshare with ITA).

There are really no other good options out of TRS. There are flights to Frankfurt with Air Dolomiti (Lufthansa group) but too late in the day for you to catch a connection from FRA to anywhere in the US.

All other flights out of TRS are with low cost airlines to European destinations that are not useful hubs for your needs.

So, unless the ITA option above works well for you, VCE is probably better, however you will need to spend the night before the flight at the VCE airport because from Trieste it is unlikely you can make it to the airport early enough for a morning flight, even if direct to ATL.

Flights from VCE to ATL are seasonal but I think they still operate in October. You need to check that.