The first available Field Manual is in the mission "Over the Top" in the War Story called "Through Mud and Blood"
After you destroy the first enemy tank follow the street and you will reach a weapon tent, to the right side of this tent is the crate and in this crate is the first available Field Manual.
Here is a video guide with all 20 Field Manuals from this war story.
*** Spoiler - click to reveal ***00:08 - #01 - Over the Top
00:48 - #02 - Over the Top
01:24 - #03 - Over the Top
01:40 - #04 - Over the Top
02:05 - #05 - Over the Top
02:34 - #06 - Fog of War
03:06 - #07 - Fog of War
03:41 - #08 - Fog of War
04:11 - #09 - Fog of War
04:40 - #10 - Fog of War
All Field Manuals in one sequence collected in Breakdown
05:02 - #11 - Breakdown
05:30 - #12 - Breakdown
05:56 - #13 - Breakdown
06:50 - #14 - Breakdown
07:18 - #15 - Breakdown
08:04 - #16 - Steel on Steel
08:44 - #17 - Steel on Steel
09:00 - #18 - Steel on Steel
09:25 - #19 - Steel on Steel
09:45 - #20 - Steel on Steel