Unfortunately, there are no near-term solutions for today's shortages. Your best bets may be to get on a vendor's "waiting list", or spend hours monitoring sources like the one mentioned by @SteveRobillard in his comment.
FWIW, an understanding of the situation may be useful in your planning. Some accounts - including one from Eben Upton - discount the "chip shortage" explanation for the current and persistent "out of stock" situation for Raspberry Pi. This article - for example - claims the "Trading Company" (run by Mr. Upton) is still manufacturing 500K units/month, but states that commercial customers have been given priority. So this isn't a "shortage" so much as a re-allocation of assets, or perhaps - as is claimed - increased demand. An older article is consistent with that explanation.
Available information suggests that perhaps changes to the Raspberry Pi organization itself may have more to do with the current shortage of RPi units than market forces in the semiconductor industry. The RPi organization has changed rather dramatically since its creation in 2009. It was founded as a charity (to serve "education", and avoid paying taxes), but according to figures published by the UK's Charity Commission the percentage of revenues actually going to "Charitable Activities" was quite small, amounting to only 10% of revenue in 2020. As a charity, the RPi organization never served much of its revenue to "Charitable Activities". The remit of the RPi organization as now disclosed seems to be substantially changed from that of an "education-oriented charity"; it is now focused on industrial applications - and profit. Only time will fully inform us of where this leads, and how it impacts future availability and cost of RPi as "hobby hardware".
But the primary motivation for this "answer" is only this: You shouldn't overlook the fact that there are masses of older PCs available in the marketplace that can also provide your niece with learning opportunities equal to or greater than the Raspberry Pi. It's certainly worth remembering that "computing" did not begin with the RPi, and that there is much to be learned beyond beyond its confines.