As good as it gets

I recently purchased a new  integrated amp. It has tube's and I wondered if there is a burn in period, or do they sound as good day one as after 4 weeks?
Always a burn in period of perhaps 50 hours and of course tubes need 45 minutes to reach optimal thermal efficiency to stabilize and sound their best.
Of course it will sound better. And not just for 4 weeks either I bet. 

Tubes are the least of what benefits from being used. Most of the sound of a tube amp is transformers, followed by caps and then circuit design and parts quality. Very little of it is the tubes themselves. But tubes are the one thing guys feel comfortable changing. So being guys they assume what they do matters. It must be the tubes.

Its not the tubes.
new tube amp needs to run for at least 50 hours music or no music, as per @celtic66 , but bare in mind, it's best to turn off tube gear when not under control for safety.
To noromance
I guess I hope it improves a little. I am comparing it to another good amp and don't hear the sound I as hoping for.
A bit of a slippery slope here.  Tubes really do make a difference, but as with everything, it's relative to parts quality supporting it all.  I spent a considerable sum on 300B tubes plus the others for my Manley preamp and it changed considerably for the better.

The Manley came stock with decent tubes, EH.  My Mahi Mahi mono blocks came with EH stock.  Upgrading those really changed and improved performance.  I don't know the level of your integrated.  Millercarbon is perhaps correct that the other pieces are more important.
I guess I hope it improves a little. I am comparing it to another good amp and don't hear the sound I as hoping for.
One thing really frustrating, people dribbling little drabs here and there. Just come out and tell us wtf is going on, so we can help, okay?WHICH amps? If you want your POC to sound like SOTA, that ain't happening. If its close and you wonder if it will get there, well then you need to tell us which amps AND describe in what ways its close or different.
I could just come out and tell you exactly what to expect in terms of changes as a component gets more hours on it. Its a very similar progression almost totally regardless of what the component is. Or even if it is a component at all- Total Contact and Omega Mats break in too.
But its a lot better if you learn to think and describe better. So we can, you know, help better.
good one Miller! I feel the same as you and get frustrated when OP’s ask for advice and don’t give enough info to allow us to provide help or an educated opinion and then there’s the OP’s who post their "system" in the most minute details which is too long or complicated to even look at.
good notes on amps should be sounding nice out of box and break-in only slightly makes it better. 
Yes but that is the answer to the question of I don't like this but they tell me it just needs to burn in, is that true? And the answer in that case is: no.
But that's not the question here now, is it?

The first question the OP asked has been answered. The second question he needs to do some homework and resubmit.
My all tube integrated amp took some time to sound it's best, whether its the internal components or tubes I can't say. Then I could begin tweaking my system for better performance. I sounds wonderful now.

After I spend some time listening to my HT system I'm always amazed and impressed when I fire up my 2 channel system for some vinyl or cd playback... even FM radio is a joy to listen to.
Tubes can take 2-300 hours to fully settle in as well as coupling capacitor 
50 hours not possible 
@geoffkait , that seems like lead substance of high temperature had traveled through brain and fried it. guns no good.
I've heard self-performed lobotomies beat brain burn-in, and work better than hi-temp lead or guns....

Less messy, considerate with your self-abuse.... ;)

If done correctly, you won't have a care in the world....or out of it, either..
after 400 hours everything in the audio chain is fully broken in. the 5-10% won't change your general impression of the amp but it always sounds a little better and less stiff after burn in.
you should swap to nos tubes which sounds much better than the modern chinese/russian crap and tune it to your liking.what tubes types are in there? anything nos 60's made is amazing compared to stock but each brand has their own voicing.

I’m no expert, but don’t designers create their products around the sound of a particular tube?

I would hope anything should sound good, and near what your expecting,pretty much right out of the box?

You ears either like what their hearing, or not. If not, move to the next choice?

I guess that's a ridiculous premise.