Welcome, Alexander! You should come check out the Safety Razor of the Month thread for this month. It's all about lather catchers like these.
As far as I've been able to determine, the "New Model" Star razor with the open front came out during 1901. Volume 68 of the trade publication The Iron Age includes a piece that announces it, but unfortunately isn't available for viewing online in Google Books. Here's the search snippet that they return, though:
Kampfe Bros., 8 to 12 Reade street New York, have just brought out a new model of the Star safety razor. Fig. 1. — Mar Safety Razor, Front View, Ready for Use. Fig. 2. — Side View, Showing Adjustable Clips for Narrow or Wide Blades. the ...
And here is an ad from the November 1901 issue of Cosmopolitan that shows it:
It was sold in that same tin for quite a number of years, however. Here is an ad from the May 1910 issue of Hardware Dealers' Magazine:
There was at least one significant design refinement during its lifetime: the blade guides went from being attached near the middle of the blade bed and slide adjustable (like the one pictured in that ad) to being fixed on a spring pivot near the front of the blade bed like yours. Roy posted a nice set of photos illustrating the two styles over in the SROTM thread. Here's one of those photos showing the two side by side (older version on the left, newer version on the right):