Desgranar is literally to remove 'grains' (corn, maize, wheat, etc), but it's also used figuratively in the sense of explain something or tell a story slowly, little by little. This is because, if you can imagine how you would remove all the grains by hand, it's a slow but methodical process, similar to a comprehensive explanation of some complex argument. In the context of your quote, 'desgranaban' goes one step further into metaphorical sense. It means the days were passing slowly, little by little, second by second. It gives a vibe of peace and quiet, almost tediousness.

Something along the lines of what Marce said in her comment... If you were poetically inclined maybe something like: The first days of the summer of 1945 were slowly ticking by. The first days ... were unfurling.

Carlos: creo que en esta frase "desgranar" tiene el significado de la opción 3 de https://dle.rae.es/desgranar?m=form2

Realmente deberías haber hecho de eso una respuesta, Marce.

It means: "take advantange of these days"