Update (after receiving many comments)
Before you read answer, note that this is hypothetical question and I am trying to answer it by creating hypothetical situations with some reasonable numbers
Short answer: Yes, hypothetically it is possible for two people to repopulate earth.
Quoting from Popsci website:
Maybe, but they'd be very busy
Hypothetically it is possible but practically it has very less probability. Let us calculate probability of repopulating earth to it's 10% population.
- Let us assume one female can give birth to 50 children throughout her reproductive life spam and assume there is no death/disease/natural crises and other factors which might restrict this 'ideal' growth.
- To get 'maximum' number of births in next generation, assume she gives birth to 1 male child and 49 female children. Probability of having that is $\left(\frac{1}{2}\right)^{50}$.
- Now again assume all 49 females gives birth to again same ratio of children (too much work for male :P). Probability of happening this will be $\left(\frac{1}{2}\right)^{50+49}$.
- If you go by same logic, you need at least 5 generations to make 10% of earth's population. That gives probability of $\left(\frac{1}{2}\right)^{50+49+49+49+49+49} = \left(\frac{1}{2}\right)^{295} = 1.57 \times 10^{-89}$
It is much lower than probability of we finding electron in nucleus :P
Now if you want to consider little bit realistic model where each couple will have two more couples and so on, It will need at least $2^{30}$ generations to repopulate to 10% of today's population. Considering average lifespan of 60 years, it will take $2^{30}\times60 = 6.4 \times 10^{10}$ years to do that. It is higher than entire biological evolution time scale.
Point of these calculations are to show that, hypothetically repopulating earth with one couple is possible but very less probable.