It'll take China 30 to 40 years to catch the US at the present trajectory. They're outrunning the US at about $200 billion per year if you assume present numbers going forward and if you believe the claimed Chinese growth figures. The gap is $7.5 to $8 trillion, while China's growth is slowing by the year.
That's ~30 year span is a best case scenario for China. The far more likely scenario, is they collide with common economic reality, with standard recessions, growth problems, debt problems, along with a continual decline in their growth rate. The last 20 years they've gotten to avoid most of those problems due to massive easy slack to fill in, in their formerly backwards economy. The debt is already there however, as they've taken on at least $50 trillion in new debt to fake their growth the last ten years (including shadow debt at the state enterprise and local muni levels). That's something they can never repeat going forward (their system is already shaking under the debt, they're constantly having to inject liquidity and restrict capital flows to keep the house of cards standing).
China has a roughly $11.5 trillion economy growing at a claimed 6.5%, with a persistent decline in their growth rate.
The US has a $19 to $19.5 trillion economy. The US is able to grow at 2.5% routinely, possibly higher in the near future.
In 2014, China's economy was $10.48 trillion. In 2015, it was $11.06 trillion. In 2016 it was $11.2 trillion.
In the time China added $1 trillion to its economy, the US added $1.6 trillion to its economy.
At 2.5% on $19 or $19.5 trillion, the US can routinely add nearly half a trillion per year to its economy.
At 6% on $11.5 trillion, China is adding $650 to $700 billion to its economy in 2018. Gradually slow their growth to even 4% to 4.5% over the next four or five years, and they may never catch the US.
I'd be willing to bet the US can sustain 2% to 2.5% growth going forward, while China can't sustain above 6%. This is especially obvious given the dramatic down curve over ten years in their growth rate. To add further to that point, there is wide agreement among economists that China aggressively lies about their GDP growth numbers, it's more likely to be closer to half the stated number.