Step 1. Vote Merkel in for 20 years

16 years, but you are essentially right

Somehow the small detail that increasing the number of people seeking jobs in certain domains (especially unspecialized occupations) is almost entirely only a win in a host country for businesses (because they can pay less for workers since adding more people to the worker pool tilts the Offer-Demand balance in the job market in their favor) and possibly a certain well-of middle class (who get cheap food delivery, cheap quasi-taxi service and cheap house-cleaners) who are politically represented by the Right not the Left, seems to fly over the heads of the mindless parrots repeating such "blame the left for immigration" slogans.

Mind you, this many decades into Neoliberalism, pretty much all "center"/"moderate" parties (i.e. the larger ones) in Europe are Rightwing Neoliberals, including the ones claiming to be "Center-Left" (notice how often they talk about what's "good for businesses" and how measures to "support businesses" including subsidies are never limited to only those businesses which have been determined to be good for Society and often help large highly exploitative/extractive businesses who evade taxes), so it's somewhat understandable that people see such supposedly Leftwing parties defending open door immigration (because as I explained above, it benefits the people who have them in their pocket) and are easily led to conclude that the Leftwing is pro-immigration.

It doesn't help that some fake-Left liberal numpties hailing from the upper middle class who parrot Anglo-Saxon Identity Politics and have no clue how the other 90% actually live, relentlessly pose as some kind of pro-immigration Leftwing when the traditional Leftwing is all about representing the local workers and the local poor and wouldn't at all put helping the workers and poor abroad above helping the ones they represent. Many people hear such fake-Lefties defending the kind of open-door immigration that won't affect them as scions of the upper middle and upper class, as some kind of duty to help other people, and think such individuals represent the Left.

In the middle of all this, immigrants (who are neither better people nor worse people that the locals) are just doing the same thing as most other people - living their lives and trying to do what's best for themselves - many having moved to another country deceived about the kind of life they could get there and how they would be accepted, only to work in shitty jobs, having to pay through their noses for their accommodation in overinflated housing markets and be made scapegoats for accepting the invitation of certain local politicians doing for selfish reason and who aren't the ones getting the blame.