As long as a raise of income of $N docks you at most N - (whatever you consider minimum wage) dollars in welfare, you won't be outright disincentivized from working.
Simplified analysis, goal is situation C. Let's say my monthly welfare income is $1000.
A. I start earning $200. My welfare decreases by $200. Why don't I just stay on welfare?
B. I start earning $200. My welfare decreases by $300. I've lost $100, a penalty for working.
C. I start earning $200. My welfare decreases by $100. I now have an incentive to work. Over time, this leads to a future situation where I gradually earn much more than I could ever with welfare.
Also consider: What if I find $1000 sufficient to live on? What about $1100?
I start earning $200. My welfare decreases by $200. My expenses increase by $100 (transportation to/from work, childcare while at work, clothes specifically for work, etc).
Once you realize that work usually has more costs than just time A and B become the same.