Here’s a guide for climbing Shasta.
Apparently Shasta can be climbed without technical gear (ropes, jumars, carabiners, pitons, wedges, etc.), but ice axes and crampons are recommended for all routes.
I took a snow-mountaineering course with the Sierra Club and learned how to do an ice-axe arrest and other related skills. Perhaps they still offer such courses.
I’ve summited Mount Whitney and crossed over the Thorong La pass (17,700 feet) in the Nepalese Himalayas.
Basically, the only conditioning I did for those hikes was walking and sprinting up several flights of stairs, two-steps at a time, while wearing heavy hiking boots.
Perhaps you can warm up for the ascent by hiking on some trails near you.
I warmed up for my Himalaya trek by backpacking up to Temple Crags near the Palisade glacier in the eastern Sierra Nevada.
Shasta is a beautiful peak- I’m sure you’ll have a great time and see some awesome views!