It is almost certainly not a Chinese proverb as it follows a common linguistic template that has been seen to evolve over the last century or so and only more recently claimed as Chinese in origin. The earliest reference I can find that uses the exact formulation is from an article in The Cleveland Plain Dealer on March 19, 1967 “Negro Help for Negroes Under Way”, Page 9A
But the template goes back farther - The St. Louis Post Dispatch used the phrase "The best time for transplanting trees is in the fall. The next best time is now." in April 2, 1902. The Centre Democrat from Bellefonte, PA used "Spring is the best time for setting strawberry plants. The next best time is now." on 18 August, 1881. These all seem to be referencing the same or similar idea, using the same structure.
The earliest that I have found the phrase attributed as a Chinese proverb was in 1985 when former Nebraska state Sen. Maurice Kremer was said to be fond of repeating an allegedly Chinese proverb: "When is the best time to plant a tree? Twenty years ago. The second-best time is today." Others who have searched claim not to find an earlier reference attributing this phrase to a Chinese proverb.
After that, it more regularly came to be referred to as a Chinese proverb - but with it only being described that way nearly 20 years after it earliest appeared in print, and before that there were other variations on the theme in common use, it seems more like a folksy aphorism from rural America than a Chinese or African proverb.
We might note, though, that if coming from rural America, it's not implausible that it originated as an African proverb which source was subsequently forgotten. I've found no clear evidence of that, however.