I won't try and give you a sliver of hope cause this isn't what it's meant to be.
But I will say that my next door neighbour had a daughter 2.5 years ago even though her tubes were tied, burnt and cut. She had no medical intervention.
It could happen, but it's very very slim. So your best bet, as the above posters said, is medical intervention
It's got an even lower fail rate than most contraception (less than 1% fail, and almost 75% of those failures occurred within a year of the initial operation to "tie the tubes")....so imagine someone asking "I'm taking my birth control pills EVERY SINGLE DAY AND USING A CONDOM that never breaks... but I'm trying to get pregnant, is it possible?"
Well, yeah. it happens. rarely. But...it's definitely not something to invest your time or hopes in. You're going to need to get the reversal. I've seen places offer it as low as $6000 or $7000...which isn't cheap, but they usually offer financing.
No. You need medical intervention to conceive. Your choices would be surrogacy, adoption, reversal or IVF.
There will of course be those who post that this person got pregnant after, or they know someone who did but failure is NOT common and shouldn't be considered. Sterilization should not be thought of as anything but permanent.