You should be able to get a decent contact print without too much effort although it does use paper. It isn't wasted, it's part of the process, like the marble that Michelangelo removed.
If I may risk insulting my betters, I'll outline the process.
Make a sandwich of paper and neg, emulsion to emulsion and clamp them together, using either a heavy sheet of glass or a contact printing frame. Some frames designed for neg proofing have all clear glass.
Use a medium grade of paper or choose a medium filter.
Set your timer to some convenient interval (I use four seconds) and place the sandwich under your light source.
Take a piece of card that will easily cover the whole neg.
Expose the whole neg to one burst of light. Now cover up a portion of it. Give it another burst. Cover up another strip, moving across the neg and giving successive bursts until the whole neg is covered by the card. Four to six bursts is convenient.
Develop the paper according to the instructions on the packet, erring, if you must, on the side of generous development. Do not snatch the print when it "looks right". It won't be right. Stop and fix the print, and give it a brief wash. Squeegee it dry and choose the strip that looks best. If the best print is at either end, you cannot be sure that the next one along would be even better, so you must do another strip, just the same but increasing or decreasing the time of the burst. Do it all again. If you can't decide between two strips, you will have to make another test, although with experience you will be able to judge much better and make an educated guess..
While you are examining the test strip, decide if you've chosen the best contrast grade. Are the highlights burnt out or the shadows blocked? If so, you may like to try another strip at a different grade. As you can see, the process consumes paper as a printer consumes ink.
(Some people prefer to make test strips by beginning with the whole sheet covered and some use a geometric progression for the intervals. Discussion for another day, perhaps.)
Finally, you are ready to make a print. It's best to replicate the correct number of bursts rather than add them up into one burst, because the paper is subject to something called the intermittency effect (so is film, as discussed by Ian with his windy pictures) Some lamps may not be uniform in their output over short periods. Develop the paper properly and don't snatch it.
There is something called "dry-down" that makes prints look a little different from the way they looked when wet. You might encounter this, and you will need to learn how to compensate for it, on another day, but nevertheless you should be holding a perfectly nice print in your hands. It may not be an Edward Weston, but he'd had a lot of practice and probably a capacious waste-paper basket under the bench.
Now you might want to create an even better print by making fine adjustments to your process.
You will get better at this. You really will. Much better.
For the moment, hang on to your test strips to review what you did. You don't have to keep them forever unless the V&A has asked you to.
Finally, may I risk even an greater insult by suggesting that if all this doesn't work, the problem may lie in the neg. I've discovered that exposure and development for scanning are not quite the same as for wet printing.
A final, final thought. Have you checked your safelights?
If anyone here has better advice, I'm very happy to be corrected.
test strips will.