In the future we can use longer wavelengths to look further into the early universe, but not further back in time.
The problem with using longer wavelengths to look further back in time than the CMB is that the universe was opaque at that time. For the first roughtly 370,000 years the universe was opaque. Photons would not travel far before being absorbed. At about the 370,000 year mark, the whole universe cooled down enough to become transparent. The universe would have been awash with photons colliding with the plasma and being re-emitted at the temperature. As the 370,000 year mark neared the mean distance between being absorbed and re-emitted was only on the order of 100 light years. Very quickly this changed to be the size of the observable universe making the universe transparent. The problem with seeing further back in time is that something emitted at the 369,900 year mark would have likely been absorbed within 100 years.
The expansion of the universe has caused those wavelengths to increase so that radiation now peaks at around 900 micrometers, and we are seeing further into the early universe. In another 13 billion years if everything goes how we think it will, the cosmic background radiation from the 370,000 year mark will have been redshifted even more into the radio wavelengths and we will see further, but only to the same time.
Imagine a straight line pointing from the Earth (A) out into the universe to
other points in the early universe that existed 370,000 years after the big bang along with the light created by that point at the 370,000 year mark as a lower-case letter (i.e. b). Here we see the light is at the point where it was emitted. Any light emitted before this from point B would have been absorbed and re-emitted (scattered) before it got to A.
abcdefg
ABCDEFG
Imagine a dense fog where you can only see a few feet in front of your face. the light 'g' at G would get absorbed before F and re-emitted, so there is no way to see further into the past than this time. As the universe dropped below 3000K, the universe quickly became transparent and the CMB we see today is from that time.
As the universe expanded, we could see further and further into the universe, but only back to the time when recombination occurred. Imagine enough time has passed that we are seeing light from C when recombination occurred and the universe has been expanding. The photons from C-G have been making their way towards A. We now can see what has been going on at B since the last scattering and can see the light from C at the last scattering. We also see that B is moving away from us. However, the light from F and G at the last scattering is actually further away from us than it was at the time because the universe is expanding too fast. We will never be able to see that light.
ABCDEFG (original distance)
c-d-e-f-g (light from last scattering)
A-B-C-D-E-F-G (current distance)
If we continue further into the future:
ABCDEFG (original distance)
d--e--f--g (light from last scattering)
A--B--C--D--E--F--G (current distance)
Notice the light 'f' is not getting any closer to us. This is the cosmic horizon. Assuming this is the current time, the light 'd' has been travelling towards us for 13.8 billion years and has redshifted from infrared into microwaves. We will eventually be able to see 'e' when it has redshifted further into radio waves. However this is not seeing further into the past, the light 'e' was emitted 400,000 years after the big bang at the same time as 'd', just in a different location.