Does your chapter do bid day buddies (Rose sister/ Squirrel sis in AGD perhaps?)? How long until bigs and littles are matched? Who has more say in determining the matchup (Do you pick them more or do you they pick you more?) All of these things will play a role in getting a little.
Spending time is key with anyone you want to be your little. Have lunch together, study together if you are in any of the same classes, invite her to go shopping with you, text her after she has an exam to see how it went, be there for her! Spending money on gifts is not as critical (at least I think so), but cards are nice! I've noticed that often women in my chapter will say they want a little, they'll get a heart sister, but then they don't spend time with her, and of course, the new member wants someone else as her big!
My SK family jokes that I "put together" our family. I completely fell in love with the PNM would would later become my little the first time I met her. We were both sophomores when she joined (I joined the previosu spring as a freshman) and she'd actually older than me, so we didn't have a traditional "big little" relationship, but we instantly clicked and knew we would be friends for a long time. The next year, on bid day I met my future grandlittle and introduced her to my little shortly thereafter. The next semester I met my future great grandlittle and knew she had to be in our family. We have a new addition and 5 generations that are very close.
