Light focusing on long distances

If you make the input beam size big enough you can, but you would probably have to make the beam so large it would be impractical.

One can derive an expression for the location of the waist (focus) of the Gaussian beam behind a lens, as a function the beam waist location in front of the lens. The maximum distance for the location of the waist behind the lens (sometimes refered to as beam throw) is given by the focal length plus the Rayleigh range $$z_{rm out} = f + z_{R,{rm out}} = f + frac{pi w_{rm out}^2}{lambda} , $$ where $w_{rm out}$ is the beam waist radius behind the lens. This condition is obtained when the input waist is also located at the focal length plus the input Rayleigh range from the lens. If the beam behind the lens has a large size, then the Rayleigh range would also be large. The size of the output Gaussian beam behind the lens under maximum beam throw conditions, is given by $$ w_{rm out} = frac{flambda}{sqrt{2} pi w_{rm in}} , $$ where $w_{rm in}$ input beam waist radius in front of the lens, and the output Rayleigh range under these conditions, is given by $$ z_{R,{rm out}} = frac{f^2}{2 z_{R,{rm in}}} , $$ where $z_{R,{rm in}}$ is the input Rayleigh range in front of the lens.

A laser beam is described as a gaussian beam. A gaussian beam is described by a spot size that changes as you move along the length of the beam. This is obvious when a laser beam is being focused. The beam is big near the lens but gets smaller as you approach the focus. The equation describing the size of the spot is:

begin{align} w(z) =& w_0sqrt{1+left(frac{z}{z_R}right)^2} z_r =& frac{pi w_0^2}{lambda} end{align}

Here $z$ is distance along the propagation direction away from the focus, $w_0$ is the waist where the beam is smallest, $lambda$ is the wavelength of light and $z_R$ is what is known as the Rayleigh range. Note that if the waist is small then the Rayleigh range is small and vice versa.

For $zll z_R$ we have that $w(z) approx w_0$. That is, within the Rayleigh range the size of the beam is approximately constant. Consider, for example, a beam with wavelenght $lambda approx 1 text{ $mu$m}$ with waist $w_0 = 1 text{ mm}$. The Rayleigh range would then be $z_R approx 3 text{ m}$. This means that for 3 meters the beam would keep a size of roughly 1 mm. However, at larger distances the beam would begin to diverge.

Looking at the equation above we see that for $zgg z_R$ we have

$$ w(z) approx frac{w_0}{z_R} z $$

That is the waist grows linearly as the beam propagates. This is what is meant by divergence of a beam. The divergence angle is given by

$$ theta = arctanleft(frac{omega_0}{z_R}right) approx frac{omega_0}{z_R} = frac{lambda}{pi w_0} $$

Where the small angle approximation holds for $lambda ll w_0$ which is typically the case. If $omega approx lambda$ then the paraxial description of a Gaussian beam begins to break down. Notice that a beam with a smaller waist diverges more rapidly.

With these equations you see that if you know $w_0$ and $lambda$ you can calculate the waist $w(z)$ everywhere. Alternatively, if you know $w(z)$ at some point $z$ outside the Rayleigh range as well as $theta$ you can calculate both $w_0$ as well as the location of the waist.

One final note. I've hinted at this above but I want to say it clearly. You can see there is no such thing as a truly collimated beam. For large enough distances beams always diverge. The relevant length scale is $z_R$. If we are only concerned with the properties of a beam over short distances ($z< z_R$) then it is possible to think about the concept of a collimated beam, but we should be careful in case we get confused.

edit: To address the question, with the equation for $theta$ as a function of $w_0$ you should be able to calculate the size of the beam at the lens for your 1 mm waist as a function of distance between the focus and the lens you are using to focus down the beam. As @flippiefanus points out, the farther away your lens is the larger the beam is going to need to be. You quickly reach technical impracticality.