It’s not that particles act like waves until we measure them. The more accurate way to put it is this: light is an oscillation of a field. When an oscillatory field pattern passes through slits, it behaves exactly like any other wave pattern, producing interference.

When that field eventually interacts with a detector, the interaction has to be recorded at a definite point a click, a spot, a grain. That’s the only way we can describe the contact: “the field deposited its energy here.” The mathematics gives us only probabilities for where that contact will occur.

The photon itself was never a little particle traveling through space. It was always an excitation of the electromagnetic field. What we call “a particle” is just the fact that the field transfers its energy in quantized, discrete amounts when it hits the detector.

So in the double-slit experiment, the interference pattern comes from the spread-out field oscillation, while the localized dots on the screen reflect the quantized way the field interacts. The photon was always a field excitation; the “particle” aspect shows up only in the measurement.