That would be very tough. You would need a new tank, even on sale, about 75-100 bucks.
Lighting is going to run at least two hundred, but you could check for some used light frames and just buy new bulbs.
What is going to really hurt is the live rock. Once again, check with your local aquarium store or club and see if someone is shutting down a tank.
A lot of stores are closing down, and you can get some pretty good deals right now.
I'm guessing this isn't including LR, just the set up, so on that list I would put:
--55 gallon tank
--stand (if you want to go really cheap, you can diy it out of a few stacks of cinder blocks with a peice of plywood on top)
--HOB skimmer (I would go with a deltec HOB MCE300 if you can find a well priced one)
--lighting (If this is for a ceph tank, you really don't need any special lighting, you could probably get by with a $50 fixture that would allow keeping of low light corals).
With all of these things, you can get them used and take a chunk off of the price that way. If you have a local reef club, you really should join it, that would help. Also check craigslist and reefcentral (although things on there aren't always as cheap).
I'd say yes, it is possible, with everything else though (LR, salt, LS, livestock) your talking 800-1000 dollars.
Unfortunately, the consumables for maintaining a saltwater tank are costly. Even if you can find someone to donate most of the equipment, salt to make 200 gallons of water runs about $50 and an inexpensive RO/DI unit is going to cost you $150 (even a donated unit would require new filters and would cost close to half the of what a new unit runs) so just being able to fill the tank, have water for weekly top offs and do a few water changes comes to $200 without buying any part of the visible setup. Even if you can scrounge on the water supply, other consumables like carbon, buffer (if you need it) and filter mateial will guarantee a necessary $200 MINIMUM just to begin.
Additionally, you will have to have something very sturdy to support the water weight and even a cement block and plywood stand (which would be very difficult to replace later) will eat into your initial money.
PS - I see L8_2_Rise also thought about the cement blocks so we must not be the only ones to have started this way
Just a reminder that the most of the cost of keeping a cephalopod is in maintenance and food, especially if your cephalopod only eats live food... So the cost of having an aquarium is not just the initial set-up.
You might want to do some reading on reefcentral and look at their nano forums to see if they interest you. A nano (usually 15 - 25 gallon tank) can be very interesting if you stock it carefully. A nano won't support much in the way of fish but can be successful with inverts. You could consider a mantis shrimp for this size tank if you wanted an unusual critter (our small mantis has done well in our 25 gallon nano cube).