The commonest way to end a child's interest in astronomy is to buy them a telescope advertising 525x on a wobbly tripod. What works is the opposite of what that product promises, and it usually costs less.
What a child needs from an instrument
Something that works within a minute, points where it is pointed, and shows the moon large and sharp. A tabletop dobsonian does all three: push it, look, done. A long refractor on a thin tripod does none of them, because the image shakes for seconds after every touch and finding anything is an adult-sized frustration.
Magnification is the trap
The boxes aimed at children lead with the highest number they can justify, and magnification is the one specification that costs nothing to claim. A 60mm telescope at 525x shows a large dim blur. The number that matters is aperture, and a 76mm instrument at $79.95 with sensible eyepieces is a better present than anything advertising a magnification figure.
Binoculars as a serious alternative
A pair of 8x40 or 10x50 binoculars needs no setup at all, works in the day as well as at night, and shows the moon, Jupiter's moons and the Milky Way. For a younger child, or one whose interest is untested, it is often the better first purchase and is easier to share.
Sharing the first night
Whatever the instrument, the first night decides. Pick a clear evening with a half moon rather than a full one, so the craters stand out along the terminator, set the telescope up in daylight, and let the child find and focus it themselves. What holds a child's interest is doing it, not being shown it.
Questions people ask about telescope
What telescope should I buy for a child?
A tabletop dobsonian, or binoculars if they are young. Avoid anything sold on magnification, which is where the disappointing instruments live.
How much should a child's telescope cost?
The printed figures here start at $79.95 for a real 76mm instrument. Spending less usually means buying a toy that will end the interest rather than start it.
Are binoculars better than a telescope for a child?
Often, for a first instrument: no setup, usable in daylight, easy to share, and they show plenty of the night sky.