You are looking at the wrong number. MTBF is 1/failure rate, which is the number of failure expected per unit of time at some specified confidence interval (typically 95%). This tells you nothing about whether your engine is about to fail. The number you want is the probability of failure at some specific time t - this is called the "Hazard rate". Engine failure is a "complex" event - one which can result from multiple cuases each or which has a different probability density function. In such cases the Central Limit Theorem tells us that the overal failure probability density function will approximate to an exponential distribution (the more the number of failure modes the closer the approximation). From the point of view of your question this is bad news, because the Hazard Rate for an exponential distribution is constant.
What does this mean? Well it tells you that unless there is a specific cause which has a higher probability just after take off (eg carb icing or birdstrike) the probability of a random failure occurring just after take off is no more or less than at any other time.
HTH,
PDR