No, unfortunately you can't operate on any amateur band without a license, except under the direct supervision of a licensed ham. You can listen, though, and if you're trying to learn, that is probably the best idea. If you've got a transceiver, just disconnect the mic and hide it someplace so you won't be tempted to transmit without a license.
As a Technician, your HF privileges are pretty limited - 10 meters is the only place where you can operate on voice, and you can only use SSB between 28.3 and 28.5 MHz.. You can do CW on the 80, 40, 15 and 10 meter bands and digital modes on 28.0-28.3. When 10 is open, it's a worldwide DX band, but 10 is usually only open in the daytime, and only when the sunspots are high. So, a General license is what you want to be able to do voice and digital modes on the other HF bands, particularly if you want to operate much at night.
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