GPS Almanac versus Sky Search
Most receivers these days work very well without the almanac.  Except in very weak signal conditions (or very strong interference conditions) they can typically acquire and start tracking all satellites in view within a small handful of seconds from a cold start, i.e. without any prior information on the receiver's position and time and without any almanac or ephemeris data.  This rapid acquisition may be with the aid of many traditional hardware correlators working in parallel, extended "multi-tap" hardware correlators, or FFT techniques** that allow the entire code phase space to be searched simultaneously.

Time To First Fix is then dominated by the time it takes to receive sufficient navigation message frames to put together the satellite ephemerides.  This can vary from 18 to 36 seconds depending on where in the broadcast cycle the receiver happened to be turned on.

Andreas makes good points about the solution quality improving after waiting for the ionosphere and UTC correction data.

For your application that needs a single daily fix and is very energy sensitive - in case you don't actually need to use the position/velocity/time information in the embedded device, but merely need to log it and be able to determine the P/V/T later, you can use a very low hardware footprint, low power technique that simply records a few milliseconds of RF baseband data (about 50 kB worth) for offline postprocessing.  This expired patent outlines the principles, and I have published open-source code to perform the postprocessing, though it is not well documented for new users.  I could probably be persuaded to tidy it up and write better docs.

** I have no idea why the this paper was considered publishable, it is has been a well-known technique for years, but this is at least a conveniently linkable explanation