Yes, essentially that is what the laws of physics as we understand them lead to as a conclusion[0].
An equivalent view is that the whole universe is a static object, including "the future" just the same as the "the past".
At first this seems difficult to accept, but if you spend some time thinking about it and thinking of the laws of physics, even the intuitive ones such as classical mechanics, it's actually difficult to imagine an alternative. How could a law even look like that allowed some agents (humans? mammals? all living things? all things in general?) any amount of behavior that is not pre-determined by the past? Could a billiard ball that is hit by the tip of the cue decide not to move? And if the billiard ball can't, why could you?
Try to imagine your brain in that moment of decision: this one neuron may fire or not. If it fires, you'll watch the Lego movie right now, if it doesn't you'll eat some candy corn instead. Looking even deeper, inside that neuron, some electro-chemical processes are building up a particular neuro-transmitter - if they build up enough, the neuron will fire, otherwise it won't. Looking even deeper, photons are "flying" around between electrons and nuclei - if one gets absorbed by this electron, the potential will be met, otherwise it won't. Who could decide whether the photon is absorbed or not, except for the past states of the photon, the neuro-transmitter soup, the neuron, the brain? How would that extra decision be factored into the laws of motion of the photon?
Of course, there is always the possibility of postulating extra-physical notions, such as God or the simulation hypothesis, that would not necessarily bend to any of the laws of physics, and are not required to be understandable in any sense. It's also possible to believe that there exists some kind of law of free will and that we have just not come to understand it yet, though maybe some day we will.
[0] though possibly there is some pure randomness built-in depending on the what the solution will turn out to be for some problems in Quantum Mechanics (the measurement problem and its possibly random outcomes), and on your preferred interpretation of it. This doesn't fundamentally help or hinder determinism, it just means that instead of a single fixed outcome being pre-determined, some dice are thrown and one of many possible outcomes happens. The Lego movie, candy corn, Youtube, they are all predictable from the initial conditions at the Big Bang, but they are just not uniquely determined.