Were there published suggestions, or otherwise discussed, that the universe could be expanding before Edwin Hubble observed that more distant galaxies indeed have higher redshift (1929)?
Yes. De Sitter published expanding cosmological models in March 1917 in which there was a cosmological constant. Friedman published his models in 1922. People didn't take this sort of stuff very seriously at the time. This kind of speculation was not considered mainstream science.
The first Doppler shift of a galaxy was discovered in 1912: a blueshift for the Andromeda galaxy. By 1914 Slipher had realized that most galaxies had red shifts. His work was greeted with extreme skepticism initially. The Shapley-Curtis debate on the nature of the spiral nebulae didn't take place until 1920. Mount Wilson undertook a large-scale campaign of observing spiral nebulae in 1919, and the picture of them as galaxies wasn't really solidly confirmed until about 1924.
The Cepheid distance scale dates to about 1924, so de Sitter and Friedman's models considerably predated the Hubble law. Lemaitre synthesized the various ideas and predicted in the Hubble law in 1925. Hubble confirmed it observationally in 1927.
So basically the theory and observations were developed side by side over a period of about 15 years. Hubble certainly was aware of the relevant ideas before he undertook the program of observation which, as one of its results, demonstrated the Hubble law empirically.