I won't go into a full history lesson on diapers, but know that some of the first disposable diapers were made in the late 1940s, they may look like cloth diapers but unlike their contemporaries, their special materials such as a plastic waterproof outer layer prevented leaks through the fabric, and the insides were made out of several layers of absorbent tissue sheets, which provided better absorbency than cloth. They could also be disposed off instead of needing to be washed after being used.

The diapers I used as reference for this image are specifically a pair of Pampers from the 1960s, which had this almost glossy layer of plastic as the outer cover:
https://www.youtube.com/watch?v=DMAauCK9ox8

I've been told by  marshallfox.1971 that these diapers were known as "Z-folds" as you had to fold the sides in, then fold them out again, making a 'Z' shape from the folds, then pull the top and bottom parts of the diapers out till it resembled the shape of a bowtie and then wrap it around your baby and secure with safety pins. The fit for these diapers were terrible though, as I will go into more detail in the next entry.

For a while, disposable diapers were more of a luxury item for wealthier families, but as they became more standardized and accessible to other families at lower prices, better fabrics and softer materials would be used. As the era of cloth diapers seems to be coming to an end.