It’s my understanding that no mass migrations back to Israel began until 1882. Prior to that the numbers were groups of at most a few thousand and normally just hundreds.
There is an ongoing attempt at revisionist history by anti-religious Zionists to belittle and minimize the earlier waves of religious settlers.
That the 1880s stands out is due to the influence of the British and French in the area, filling in the power vacuum left by the decaying Ottomans.