The Switch did better than the DS initially in the U.S., but that's because the DS had a weak start. When the DS Lite was released, the DS experienced the single largest and most protracted period of growth of any system ever in the U.S. market. Once you put the Switch up against post-DS Lite quarters, the DS has outperformed it considerably (only in Q4 of Year 2 did the Switch do better than the post-Lite DS). Overall, the DS sold about 8.2M in 2007, vs. about 6.5M for the Switch in 2019. That's 29.6% better for Year 3 for the DS. And the DS kept growing. Total Year 1 to Year 3 sales for the Switch are now only less than 700k ahead of what the DS did in the same time frame (and if you add in the 1225k the DS sold in Nov.+Dec. 2004, it's actually ahead of the Switch).
Unless the Switch can manage 50% YoY growth this year, that deficit is going to grow, very quickly, and considering January NPD summaries indicate the Switch is actually slightly down this year, and with no new hardware model due this year, that doesn't bode well for any significant year-over-year growth. Even a big price cut and some big game likely won't do the trick for the Switch this year. Historical sales patterns show that, in nearly cases (and in all cases with Nintendo systems), once a system has had several quarters of YoY growth and that growth ceases and turns into YoY declines, that system will have entered the terminal decline phase of its life. It's entirely possible that 2019 was the Switch's peak in the U.S., though we won't have a clear enough picture to tell for certain for at least another few months.
In Japan, the Switch has already racked up a staggering deficit against the DS. Even if we ignore the DS's 2004 sales, the Switch is running a deficit of nearly 8 million units against the DS. The Switch is even trailing the 3DS by a decent amount, and the 3DS also fell well short of the DS. Unless it pulls some mind-blowing figures over the next 3-4 years that put 2019 sales levels to shame, there's no way in hell the Switch is going to even come close matching the DS in Japan, much less surpassing it.
And if VGC data is any indication, the Switch will have to quadruple its current LTD sales figures in Europe to just tie the DS. No system has ever been that back-loaded, so it'd be safe to file that under "Not Going to Happen."
TL;DR: A cursory glance at the sales data demonstrates quite clearly that the odds of the Switch surpassing the DS are close to nil.