Root vegetables, like beets, do not necessarily need to grow from seed, and can flourish indoors.

Slice off the top portion of a beet with a kitchen knife. Take no more than one-third of the beet.
Fill a glass, mug or bowl with water. Place the beet top into the water, with the cut side facing downward.
Set the glass on a windowsill, counter or table that is close to the window, so the beet top will receive adequate sunlight.
Change out the water every few days to prevent bacterial growth and keep the water fresh.
Harvest the beet greens once they begin to grow greens and shoots. The beet will produce greens for several weeks.
Things You Will Need
Beet
Kitchen knife
Water glass
Tip
If the beet top sinks, rather than floats on top of the water's surface, switch to a shallow dish instead of a cup or bowl. If you would like your beet top to root for later planting, apply rooting hormone to the cut surface and grow it in potting soil instead of plain water. -source

If you buy a bunch of beets, stick one in the ground and water in.
After a month or so it will be big and the main beet sticking out of the ground but very possibly with a male beets now attached.
If so, separate and replant. They just keep multiplying! I’ve been doing this for a year now

I sat a full beet over a cup so its roots were in the water and it contunually grows new leaves you can harvest. Suppose if you plant it in a pot of soil and give it enough light you can have an eternal beet that will live forever in vegetative state. Or maybe my beet is just so large it will take a few years to use up all the energy making leaves.

Yes, you can simply plant the beet and grow greens. The root will get quite tough after a growing season, so it might not be worth digging up and eating at that point. But, like you said, you can let it go to seed and gather those for next year.

If I cut the head off and put in the ground/sool how long will it take for me to get a beet? Does it only grow the green leaves by doing that?
REPLY
LILY SAYS: The beet root won’t regrow, just the greens. -source
How to grow -video

Brussels sprouts, cauliflower, broccoli, cabbage, and kale do well when planted with beets. Beets benefit these members of the cabbage family by adding essential minerals to the soil needed for the development of strong and healthy plant growth. Garlic and all members of the onion family are protective companions for beets. Many experienced gardeners mention that planting garlic with beets improves beet flavor. Garlic also emits sulfur into the soil. Sulfur contains natural anti-fungal properties, making it a helpful agent in preventing a diverse array of plant diseases caused by different strains of common soil fungi. Strongly scented culinary herbs such as thyme, hyssop, rosemary, and all varieties of mint are helpful companion plants for beets. They keep away cabbage moths, fleas, flea beetles, aphids, and rodents. Mint does double duty: it also improves the flavor of cabbage, a boon companion plant for beets. Beets are cold-tolerant, so they can be planted in early spring weeks before the last frost. Although beets do prefer full sun, they can grow just fine in a partially shaded area of the garden plot. - source https://www.thompson-morgan.com/p/beetroot-rainbow-beet-globe/tt38788TM https://store.underwoodgardens.com/rainbow-beet-mix-seeds-beta-vulgaris/v1535/