Mr Salmond revealed he was taking leadership of the party just one week ago, which is placing 32 candidates on the upcoming ballot.
The party rests on a pro-independent Scottish nationalist mandate, which Mr Salmond argues is a key reason for including the party in televised debates, saying “If the TV companies stick to their present position, every debate will be imbalanced three to two against independence. With Alba’s representation, at a stroke, the independence argument will be balanced three apiece.”
The Alba Party was not included in the first televised debate of the Scottish election campaign, which saw Nicola Sturgeon – Mr Salmond’s successor as SNP leader and First Minister – take on her rivals from the Tories, Labour, the Lib Dems and the Greens.
According to the party’s leader, membership of the party is in the thousands, and he is confident Alba Party will win more seats than the Liberal Democrats (who currently hold 5 of the 129 seats in Scottish Parliament).
Speaking at an online press conference, Mr Salmond said: “Already, after less than a week since launch, we are a national party putting up a serious challenge and can argue we have got a significant following already.
“We are firmly of the opinion at the rate of membership increase that our membership will overtake that of the Scottish Liberal Democrats.
“We expect in the coming weeks to overtake the membership of the Green Party and the Conservative Party as well, unless they of course have an unexpected surge in membership.
“I think the Alba Party has added some excitement to the Scottish political scene, I think we would add something distinctive to the political debates.
“I think more people will watch if Alba are participating than will watch if Alba are excluded in the debates.”
Speaking to journalists later on Thursday, Scottish Liberal Democrat leader Willie Rennie said: “It’s for the broadcasting authorities to decide but he can’t bully his way in to this debate, he needs to earn it.
“I’m sure the BBC and STV will be robust in their position on that.”
He said the nationalist movement has become “fragmented” while the debates around Mr Salmond over the last few weeks had been “ugly and poisonous”.
He added: “Nicola Sturgeon has effectively lost control of the nationalist movement she had a pretty firm grip on before.”
Former SNP leader, Alex Salmond, resigned from the party in 2018 amid sexual assault allegations, which the court cleared him of in 2020.
Mr Salmond has previously claimed that senior SNP figures around SNP leader Nicola Sturgeon mounted a “malicious and concerted” attempt to bring him down.