OK, let me reconstruct how you made my character, to make sure I fully understand.
[ +- ] htech version
Level 1:
Scholar: Know-0, Administer-0, Program-0
Class: Adventurer Expert/Psychic
Adventurer-E: Focus: Specialist-Administer-1: Administer-1
Adventurer-P: Precog/Oracle-0
Focus: Hacker-1: Program-1
Bonus: Trade-0
At the end of Level 1, his skills are: Know-0, Administer-1, Program-1, Trade-0
On to Level 2
Level 2:
Focus1: Specialist-Administer-2
Focus2: Hacker-2
Skill1: Precog/Oracle-1 (Terminal Reflection)
Skill2: Know-0.5
Skill3: Know-1
Skill4: Pilot-0
At the end of Level 2, his skills are: Know-1, Adminster-1, Program-1, Trade-0, Pilot-0
This matches what you have done. (I didn't know the best way to show the use of two skill points for Know-1.)
However, I can improve things if I just make a simple swap. For the Level 1 Bonus skill, I get more skills if I take Know-1 right then.
[ +- ] version two
Level 1:
Scholar: Know-0, Administer-0, Program-0
Class: Adventurer Expert/Psychic
Adventurer-E: Focus: Specialist-Administer-1: Administer-1
Adventurer-P: Precog/Oracle-0
Focus: Hacker-1: Program-1
Bonus: Know-1
At the end of Level 1, his skills are: Know-1, Administer-1, Program-1
Level 2:
Focus1: Specialist-Administer-2
Focus2: Hacker-2
Skill1: Precog/Oracle-1 (Terminal Reflection)
Skill2: Trade-0
Skill3: Fix-0
Skill4: Pilot-0
At the end of Level 2, his skills are: Know-1, Adminster-1, Program-1, Trade-0, Pilot-0, Fix-0
This is taking advantage of two things. First, I know I am going straight to Level 2, so I can take some efficiencies like you mentioned. Now, I get the Know-1, but I get an extra skill (Fix is a placeholder) because I got the improvement in Level 1 and waited for the level-0 skills. That is a bit optimize-y, but I think that works.
Now, I could take this a step farther and gain a level-2 skill at Level 2! I chose Administer-2 below, but it could just as easily be Program-2 instead. Whichever is more useful.
[ +- ] version three
Level 1:
Scholar: Know-0, Administer-0, Program-0
Class: Adventurer Expert/Psychic
Adventurer-E: Focus: Hacker-1: Program-1
Adventurer-P: Precog/Oracle-0
Focus: Hacker-2
Bonus: Administer-1
Level 1 Skills: Know-0, Administer-1, Program-1
Level 2:
Focus1: Specialist-Administer-1: Administer-2
Focus2: Specialist-Administer-2
Skill1: Precog/Oracle-1 (Terminal Reflection)
Skill2: Trade-0
Skill3: Fix-0
Skill4: Pilot-0
Level 2 Skills: Know-0, Adminster-2, Program-1, Trade-0, Fix-0, Pilot-0
Doing this, however, prevents me from getting Know-1 because the skills taken for Level 1 are absolutely proscribed with no variance allowed (to get me to my goal), and getting Know-1 would force me to drop Pilot. (And Fix. Fix is again a placeholder.)
Also, if I am looking at game optimization, it looks like there actually isn't a whole lot of utility for level-0 skills. It just gets you a +1 on your roll, while level-1 skills give you an additional +2. So, maybe in "version two" I should drop any/all of the level-0 skills to hammer up to a level-1 skill?