I didn't suggest immigration was the solution. It's a stopgap, and an accidental one, but one that happens to be working out in America's favor right now. If we had an immigration system like Japan's then we'd have demographic decline closer to Japan's than our own.
As for the statistics you cited, they're for permanent residency ("green cards"), not immigrant visas. Due to a few strange quirks of the US immigration system, the time it takes from visa to residency increases based on how many other immigrants came from the same country as you. A lot of these people are going to be Mexicans who have been legally residing in the country on one or more visas for the last 10-20 years.
I can't seem to find the visa data in this PDF, and the green card numbers are visa datum with time lag, so I'll continue nitpicking them. Almost half of the green cards granted are for immediate family members, and another 166k are other family sponsorships. The other immigration categories (e.g. refugees, diversity visa holders[0], etc) are less than a quarter of the total green card pool.
In terms of finding immigrants who are a net positive to society, family sponsorship is arguably a better basis for immigration than employment. There are a lot of employers who game the immigration system[1] to skirt around America's labor laws. Employers don't care about the people they bring in as long as they work for cheap and do what you tell them. So they're bringing people in with no support network beyond a company that deliberately wants to exploit them.
[0] For the same reason why America makes Mexicans wait 20 years to get their green card, people from countries underrepresented in the green card pool can apply for a special diversity visa that right-wingers love to complain about despite the fact that it makes the immigrant pool less Mexican
[1] Specifically the H-1B visa program.
Also, just to put all my cards on the table: my views on immigration are extremely libertarian. Immigration is one of the most dehumanizingly bureaucratic nonsense processes one can go through with a government. The reason why companies are able to abuse H-1B is because you can't switch jobs outside of other potential H-1B sponsors who are going to expect the same out of you. It's a literal immigrant underclass!