First, there must exist an un-levered version of the ETF or another index product, the constituents of the index are known and tradable, or an options market for the index, or other source of risk of the index exposure. The dealer that is paying the index total return on the TRS must be able to source the risk and will use one of these vehicles/market. For simplicity, let's say an un-levered version of the fund exists.
A broker/dealer/bank is the counterparty on the TRS that will be the total return PAYER of the index AND RECEIVER of the interest (LIBOR + spd). On a TRS, one is paying the dealer to put the asset on their balance sheet, thereby providing the leverage (loan) to the ETF.
Let's assume that L=2 in your product. When the ETF receives an investment into the fund, as you say, they can buy index constituents and get 1x A exposure to the index. They then get another 1x A exposure via a TRS with a dealer to RECEIVE total return and PAY financing (LIBOR + spd). The dealer will in turn buy the A exposure to the unlevered index fund as the source of the risk from which they will pay the return of the index. As the asset is paid for by the dealer and put on their balance sheet, they will charge the ETF interest on the amount used to purchase the asset (LIBOR +spd).
The financing (LIBOR + spd) is embedded in the performance of the levered ETF as it is paying this to the TRS counterparty. You should see that levered versions of the index ETF are underperforming L times the index by this financing charge on the levered portion of the ETF.
The reason why the levered ETF needs to be rebalanced daily is as an exchange traded fund, it will be bought and sold throughout a trading day. At the end of the day, there will be a net BUY or SELL of the ETF, requiring a net creation or redemption of the ETF. The ETF sponsor or authorized participant will need to buy or sell the index depending on the net of the purchases and sales to create or redeem the net units of the ETF. They will also need to adjust exposure on leveraged portion of the ETF by adjusting the notional on the TRS to maintain the leverage ratio. (The dealer/counterparty on the TRS will in turn adjust their exposure/risk source to the underlying index as well.)