At the beginning, even Abigail tries to tell Parris that Betty is not bewitched, that Tituba was only singing "her Barbados songs" while the girls danced innocently, and all suspicions of witchcraft are false.
Abigail: Uncle, we did dance; let you tell them I confessed it--and I'll be whipped if I must be. But they're speakin' of witchcraft. Betty's not witched. (Act 1, Scene 1)
The first person to make an accusation in the context of witchcraft and/or immoral behavior is Mrs. Putnam. After Abigail tells Parris that the suspicions of witchcraft are false, Mrs. Putnam arrives and notes that these developments are "a stroke of hell" and she then claims that Mrs. Collins saw Betty flying (as witches do) over Ingersoll's barn. Parris tries to argue with her but Mrs. Putnam is certain that witchcraft has come to Salem. She adds that a witch was found in Beverly the previous year. Mr. Putnam agrees with his wife, adding "There are hurtful, vengeful spirits layin' hands on these children."
Mrs. Putnam reveals that she thinks Tituba can speak to the dead and had even sent her daughter, Ruth, to Tituba to speak to the spirits and possibly find out if the seven babies she (Mrs. Putnam) lost were murdered, perhaps by witches. However, the Putnams do not mention a specific name. So, while it is the Putnams who ignite the suspicions of witchcraft, they only suspect that Tituba had some role in conjuring the Devil as she was attempting to conjure Mrs. Putnam's dead babies.
Although Abigail initially determines to tell the truth (dancing and playful conjuring), she feels pressured and begins to implicate Tituba when Hale continues to question her. Abigail claims that Tituba made her drink blood and then she starts to accuse Tituba of other things.
Abigail: Sometimes I wake and find myself standing in the open doorway and not a stitch on my body! I always hear her laughing in my sleep. I hear her singing her Barbados songs and tempting me with--
Tituba refutes the accusations. But feeling pressured, she eventually falsely accuses Sarah Good and Goody Osburn.
The Putnams ignite the suspicions of witchcraft. Abigail is the first to accuse a specific person (Tituba) of engaging in witch-like activity. And it is Tituba who first accuses other women of witchcraft. At the end of Act 1, Betty and Abigail make more accusations of witchcraft.
(Note: technically, the first implication of an accusation of witchcraft comes from Mrs. Collins via Mrs. Putnam's story. But Mrs. Collins is not a main character and within the context of the play, the more meaningful accusations occur in the presence of the religious authorities: Hale and Parris.)