For 5e as of Chrome Flesh the ways to get + to Initiative/Initiative Dice that do not involve magic are as follows:
Qualities:
Lightning Reflexes (20 Karma) - +1 Ini/ +1 Ini Dice +1 Defense Die Does not Stack with INITIATIVE enhancers.
Adrenaline Surge (12 Karma) - Special Mention, lets you go first the first turn of combat automatically.
Chrome:
Wired Reflexes - Your standard jittery wireman, Reaction and Initiative Dice. Can stack with…
Reaction Enhancers - Increases REA. Can stack with above with both wireless enabled
Move by Wire - Reaction, Initiative, Initiative Dice (at higher ratings) AND skillwires all for the cost of having muscles constantly in a seizure state!
Note, of the Chrome options only Reaction Enhancers really seem like they'd be good for your character
Bioware:
Synaptic Booster: Expensive, but basically Wireless Reflexes made of actual cells. Stacks with no REA or Ini boosters though. Sadface.
Cerebellum Booster: Direct increase to Intuition.
Suprathyroid Gland: Adds to, among other things, Reaction. Doesn't stacks with anything that doesn't explicitly NOT stack.
Boosted Reflexes: Cheap, Essence Intensive, Stacks with no other ini enhancers and only adds 1 Ini Die. MAY stack with Reaction Enhancers and Cerebellum Boosters depending on interpretation.
Geneware:
Synaptic Acceleration: consider it a slightly cheaper Synaptic Booster that can only gain one level. Note that it actually simply adds Initiative and Dodge dice instead of Reaction. Also note RAW, can also be interpreted to stack with Reaction Enhancers and Cerebellum Boosters, but not Initiative boosts.
Reaction Optimizations: Gives you +1 Initiative if you own any level of Reaction Enhancers. Does not stack with other ini boosts.
Drugs:
Cram: small ini boost, long preptime, long duration, painful crash.
Jazz: medium ini boost, fast preptime, short duration, minimal crash.
Kamikaze: Medium ini Boost, lots of physical att boosts, Short Duration, Big Crash
Betameth: +2 Rea +1 Int, medium preptime, long duration, painful crash.
K-10: Big INi Boost (no die though), huge buffs to combat skills. DO NOT RECOMMEND CRASH SUX.
Again, for long term game, Do not recommend drugs for your character.