The convention is that positive time is the future and negative time is the past. If you assume this convention then you can explicitly show that Newton's laws are time reversible or time symmetric.

A ball is thrown.

$y=v_{oy} - \frac{g}{2} t^2$

$x=v_{ox}t$

A film of the thrown ball is played in reverse. $t \to -t$

$y=-v_{oy} - \frac{g}{2} t^2$

$x=-v_{ox}t$

In both cases, $m\frac{dy^2}{dt^2}=-mg$.

If you watch a film of a ball moving along such a path then you can't tell whether the film is going forward in time or backward. Both motions are consistent with Newton's Laws and nothing looks unusual if time is reversed.

The convention is that positive time is the future and negative time is the past. If you assume this convention then you can explicitly show that Newton's laws are time reversible or time symmetric.

A ball is thrown.

$y=v_{oy}t - \frac{g}{2} t^2$

$x=v_{ox}t$

A film of the thrown ball is played in reverse. $t \to -t$

$y=-v_{oy}t - \frac{g}{2} t^2$

$x=-v_{ox}t$

In both cases, $m\frac{dy^2}{dt^2}=-mg$.

If you watch a film of a ball moving along such a path then you can't tell whether the film is going forward in time or backward. Both motions are consistent with Newton's Laws and nothing looks unusual if time is reversed.

So, yes, it is ultimately a convention, but it is a convention that works. Obviously, you could completely reverse the convention and that would be consistent with Newton's Laws.