You probably took a seed from an F1 hybrid.
F1 hybrids do produce "plants", but little to no fruit.
They are genetically modified plants - a big thank you to Monsanto at this point.
I have currently bought 50 mango trees from my trusted plant dealer and am currently planting them.
3 different varieties, about 3 years old, each one normally costs THB 230, with a discount now THB 210.
Fruit trees usually produce fruit between the ages of 3-5.
So I have gained time.
What you can do with your mango is use it as a "rootstock" for a fruit tree.
As you correctly suspect, the tree is cut down and a fruit variety is grafted onto it.
The ideal time for this is always the end of the dormant period and the beginning of the growth period.
In Thailand, I would describe the dry season as the dormant period - until about the end of January, before the mangos start to bloom.
The growth phase begins at the beginning/end of May - when the rainy season begins and the fruiting period is over.
I would therefore assume that the ideal time for grafting is April.
You can either try your luck now or wait until the end of March next year and then graft.
During this time you could also practice grafting on various plants in advance.
Roses, vines, limes, neem - basically everything that naturally grows quickly and easily.