As far as we can tell, the four-dimensional space-time continuum is unbounded in the space directions (space is infinite) the time dimension seems to have a singularity (about 13.8 billion years before now) and so it is impossible to talk in a sensible way about events before that time. We would normally say that the universe and time itself started at that point, and so any statement about "before the big bang" is completely meaningless. There are other possibilities, such as "eternal inflation", but they are rather speculative, with little positive evidence.
In the other direction, into the future, time seems to be unbounded, though this is less certain, it depends very precisely on several cosmological parameters, whose values are not yet certainly known.
So our current best hypothesis is that time is finite into the past, but infinite into the future.
Energy is locally conserved within the universe, but don't apply such reasoning to the formation of the universe. Indeed the whole concept of physics ceases to operate at that singularity. The basis of nature as cause-and-effect cannot operate at a singularity.
If space is indeed infinite, and the universe is homogenous and isotropic, then the total mass-energy of the universe could be infinite. However the potential gravitational energy might be negative infinite, and so the total energy of the universe might be zero, leading to Hawking's observation that "the universe is the ultimate free lunch".